8.4: Developing Mission, Vision, and Values
What’s in It for Me?
Reading this chapter will help you do the following:
- Understand the roles of mission, vision, and values in the planning process.
- Understand how mission and vision fit into the planning-organizing-leading-controlling (P-O-L-C) framework.
- See how creativity and passion are related to vision.
- Incorporate stakeholder interests into mission and vision.
- Develop statements that articulate organizational mission and vision.
- Apply mission, vision, and values to your personal goals and professional career.
As you are reminded in the figure, the letter “P” in the P-O-L-C framework stands for “planning.” Good plans are meant to achieve something—this something is captured in verbal and written statements of an organization’s mission and vision (its purpose , in addition to specific goals and objectives). With a mission and vision, you can craft a strategy for achieving them, and your benchmarks for judging your progress and success are clear goals and objectives. Mission and vision communicate the organization’s values and purpose, and the best mission and vision statements have an emotional component in that they incite employees to delight customers. The three “planning” topics of your principles of management cover (1) mission and vision, (2) strategy, and (3) goals and objectives. The figure summarizes how these pieces work together.
As of 2010, Xerox Corporation (NYSE: XRX) is a $22 billion, multinational company founded in 1906 and operating in 160 countries. Xerox is headquartered in Norwalk, Connecticut, and employs 130,000 people. How does a company of such size and magnitude effectively manage and motivate employees from diverse backgrounds and experiences? Such companies depend on the productivity and performance of their employees. The journey over the last 100 years has withstood many successes and failures. In 2000, Xerox was facing bankruptcy after years of mismanagement, piles of debt, and mounting questions about its accounting practices.
Anne Mulcahy turned Xerox around. Mulcahy joined Xerox as an employee in 1976 and moved up the corporate ladder, holding several management positions until she became CEO in 2001. In 2005, Mulcahy was named by Fortune magazine as the second most powerful woman in business. Based on a lifetime of experience with Xerox, she knew that the company had powerful employees who were not motivated when she took over. Mulcahy believed that among other key businesses changes, motivating employees at Xerox was a key way to pull the company back from the brink of failure. One of her guiding principles was a belief that in order to achieve customer satisfaction, employees must be treated as key stakeholders and become interested and motivated in their work. Mulcahy not only successfully saw the company through this difficult time but also was able to create a stronger and more focused company.
In 2009, Mulcahy became the chairman of Xerox’s board of directors and passed the torch to Ursula Burns, who became the new CEO of Xerox. Burns became not only the first African-American woman CEO to head a Standard & Poor’s (S&P) company but also the first woman to succeed another woman as the head of an S&P 100 company. Burns is also a lifetime Xerox employee who has been with the company for over 30 years. She began as a graduate intern and was hired full time after graduation. Because of her tenure with Xerox, she has close relationships with many of the employees, which provides a level of comfort and teamwork. She describes Xerox as a nice family. She maintains that Mulcahy created a strong and successful business but encouraged individuals to speak their mind, to not worry about hurting one another’s feelings, and to be more critical.
Burns explains that she learned early on in her career, from her mentors at Xerox, the importance of managing individuals in different ways and not intentionally intimidating people but rather relating to them and their individual perspectives. As CEO, she wants to encourage people to get things done, take risks, and not be afraid of those risks. She motivates her teams by letting them know what her intentions and priorities are. The correlation between a manager’s leadership style and the productivity and motivation of employees is apparent at Xerox, where employees feel a sense of importance and a part of the process necessary to maintain a successful and profitable business. In 2010, Anne Mulcahy retired from her position on the board of directors to pursue new projects.
Case written based on information from:
Bryant, A. (2010). “Xerox’s new chief tries to redefine its culture,” New York Times,
Forbes. (2010). “Profile: Anne M. Mulcahy,” https://images.forbes.com/lists/2005/11/VI6W.html .
Fortune. (2006). “50 most powerful women,” CNN Money, http://money.cnn.com/popups/2006/fortune/mostpowerfulwomen/2.html .
http://www.nytimes.com/2010/02/21/business/21xerox.html?pagewanted=18dpc .
Tompkins, N. C. (1992). Employee satisfaction leads to customer service. All Business.
Whitney, L. (2010). “Anne Mulcahy to retire as Xerox chairman,” CNET News. https://www.cnet.com/tech/tech-industry/xerox-ceo-anne-mulcahy-to-retire/ .
Discussion Questions
- In terms of the P-O-L-C framework, what values do the promotion and retention of Mulcahy and Burns suggest are important at Xerox? How might these values be reflected in its vision and mission statements?
- How do you think Xerox was able to motivate its employees through the crisis it faced in 2000?
- How do CEOs with large numbers of employees communicate priorities to a worldwide workforce?
- How might Ursula Burns motivate employees to take calculated risks?
- Both Anne Mulcahy and Ursula Burns were lifetime employees of Xerox. How does an organization attract and keep individuals for such a long period of time?
Learning Objectives
- Be able to define mission and vision.
- See how values are important for mission and vision.
- Understand the roles of vision, mission, and values in the P-O-L-C framework.
Mission, Vision, and Values
Mission and vision both relate to an organization’s purpose and are typically communicated in some written form. Mission and vision are statements from the organization that answer questions about who we are, what do we value, and where we’re going. A study by the consulting firm Bain and Company reports that 90% of the 500 firms surveyed issue some form of mission and vision statements (Bart & Baetz, 1998). Moreover, firms with clearly communicated, widely understood, and collectively shared mission and vision have been shown to perform better than those without them, with the caveat that they related to effectiveness only when strategy and goals and objectives were aligned with them as well (Bart et al., 2001).
A mission statement communicates the organization’s reason for being and how it aims to serve its key stakeholders. Customers, employees, and investors are the stakeholders most often emphasized, but other stakeholders like government or communities (i.e., in the form of social or environmental impact) can also be discussed. Mission statements are often longer than vision statements. Sometimes mission statements also include a summation of the firm’s values. Values are the beliefs of an individual or group, and in this case the organization, in which they are emotionally invested. The Starbucks mission statement describes six guiding principles that, as you can see, also communicate the organization’s values:
- Provide a great work environment and treat each other with respect and dignity .
- Embrace diversity as an essential component in the way we do business .
- Apply the highest standards of excellence to the purchasing, roasting and fresh delivery of our coffee.
- Develop enthusiastically satisfied customers all of the time .
- Contribute positively to our communities and our environment .
- Recognize that profitability is essential to our future success (Starbucks, 2008).
Similarly, Toyota declares its global corporate principles to be:
- Honor the language and spirit of the law of every nation and undertake open and fair corporate activities to be a good corporate citizen of the world .
- Respect the culture and customs of every nation and contribute to economic and social development through corporate activities in the communities .
- Dedicate ourselves to providing clean and safe products and to enhancing the quality of life everywhere through all our activities .
- Create and develop advanced technologies and provide outstanding products and services that fulfill the needs of customers worldwide .
- Foster a corporate culture that enhances individual creativity and teamwork value while honoring mutual trust and respect between labor and management .
- Pursue growth in harmony with the global community through innovative management .
- Work with business partners in research and creation to achieve stable, long-term growth and mutual benefits, while keeping ourselves open to new partnerships (Toyota, 2008).
A vision statement , in contrast, is a future-oriented declaration of the organization’s purpose and aspirations. In many ways, you can say that the mission statement lays out the organization’s “purpose for being,” and the vision statement then says, “Based on that purpose, this is what we want to become.” The strategy should flow directly from the vision because the strategy is intended to achieve the vision and thus satisfy the organization’s mission. Typically, vision statements are relatively brief, as in the case of Starbucks’s vision statement, which reads: “Establish Starbucks as the premier purveyor of the finest coffee in the world while maintaining our uncompromising principles as we grow" (Starbucks, 2008). Or ad firm Ogilvy & Mather, which states their vision as “an agency defined by its devotion to brands" (Ogilvy, 2008). Sometimes the vision statement is also captured in a short tag line, such as Toyota’s “moving forward” statement that appears in most communications to customers, suppliers, and employees (Toyota, 2008). Similarly, Wal-Mart’s tag-line version of its vision statement is “Save money. Live better" (Walmart, 2008).
Any casual tour of business or organization websites will expose you to the range of forms that the mission and vision statements can take. To reiterate, mission statements are longer than vision statements, often because they convey the organization's core values. Mission statements answer the questions of “Who are we?” and “What does our organization value?” Vision statements typically take the form of relatively brief, future-oriented statements—vision statements answer the question: “Where is this organization going?”. Increasingly, organizations also add a values statement that either reaffirms or states outright the organization’s values that might not be evident in the mission or vision statements.
Roles Played by Mission and Vision
Mission and vision statements play three critical roles:
- Communicate the purpose of the organization to stakeholders
- Inform strategy development
- Develop measurable goals and objectives by which to gauge the success of the organization’s strategy.
These interdependent, cascading roles and the relationships among them are summarized in the figure.
First, mission and vision provide a vehicle for communicating an organization’s purpose and values to all key stakeholders. Stakeholders are those key parties who have some influence over the organization or stake in its future. You will learn more about stakeholders and stakeholder analysis later in this chapter; however, for now, suffice it to say that some key stakeholders are employees, customers, investors, suppliers, and institutions such as governments. Typically, these statements would be widely circulated and discussed often so that their meaning is widely understood, shared, and internalized. The better employees understand an organization’s purpose, through its mission and vision, the better able they will be to understand the strategy and its implementation.
Second, mission and vision create a target for strategy development. That is, one criterion of a good strategy is how well it helps the firm achieve its mission and vision. To better understand the relationship among mission, vision, and strategy, it is sometimes helpful to visualize them collectively as a funnel. At the broadest part of the funnel, one will find the inputs into the mission statement. Toward the narrower part of the funnel is the vision statement, which has distilled down the mission in a way that can guide the development of the strategy. In the narrowest part of the funnel is the strategy —it is clear and explicit about what the firm will do and not do to achieve the vision. Vision statements also provide a bridge between the mission and the strategy. In that sense, the best vision statements create tension and restlessness regarding the status quo—that is, they should foster a spirit of continuous innovation and improvement. For instance, in the case of Toyota, its “moving forward” vision urges managers to find newer and more environmentally friendly ways of delighting the purchaser of their cars. London Business School professors Hamel and Prahalad describe this tense relationship between vision and strategy as stretch and ambition. Indeed, in a study of such able competitors as CNN, British Airways, and Sony, they found that these firms displaced competitors with stronger reputations and deeper pockets through their ambition to stretch their organizations in more innovative ways (Hamel & Prahalad, 1993).
Third, mission and vision provide a high-level guide, and the strategy provides a specific guide to the goals and objectives, showing the success or failure of the strategy and satisfaction of the larger set of objectives stated in the mission. In the cases of both Starbucks and Toyota, you would expect to see profitability goals, in addition to metrics on customer and employee satisfaction and social and environmental responsibility.
Key Takeaway
Mission and vision both relate to an organization’s purpose and aspirations, and they are typically communicated in some form of brief written statements. A mission statement communicates the organization’s reason for being and how it aspires to serve its key stakeholders. The vision statement is a narrower, future-oriented declaration of the organization’s purpose and aspirations. Together, mission and vision guide strategy development, help communicate the organization’s purpose to stakeholders and inform the goals and objectives set to determine whether the strategy is on track.
Exercises
- What is a mission statement?
- What is a vision statement?
- How are values important to the content of mission and vision statements?
- Where does the purpose of mission and vision overlap?
- How do mission and vision relate to a firm’s strategy?
- Why are mission and vision important for organizational goals and objectives?
Learning Objectives
- Understand the role of mission and vision in organizing .
- Understand the role of mission and vision in leading .
- Understand the role of mission and vision in controlling .
Mission and vision play such a prominent role in the planning facet of the P-O-L-C framework. Beyond the relationship between mission and vision, strategy, and goals and objectives, one will expect to see mission and vision being related to the organizing , leading , and controlling aspects as well. Let’s look at these three areas in turn.
Mission, Vision, and Organizing
Organizing is the function of management that involves developing an organizational structure and allocating human resources to ensure the accomplishment of objectives. The organizing facet of the P-O-L-C framework typically includes subjects such as organization design, staffing, and organizational culture. Regarding organizing, it is useful to think about the alignment between the mission and vision and various organizing activities. For instance, organizational design is a formal, guided process for integrating the people, information, and technology of an organization. It is used to match the form of the organization as closely as possible to the purpose(s) the organization seeks to achieve. Through the design process, organizations act to improve the probability that the collective efforts of members will be successful.
Organization design should reflect and support the strategy—in that sense, organizational design is a set of decision guidelines by which members will choose appropriate actions, appropriate in terms of their support for the strategy. As you learned in the previous section, the strategy is derived from the mission and vision statements and from the organization’s basic values. Strategy unifies the intent of the organization and focuses members on actions designed to accomplish desired outcomes. The strategy encourages actions that support the purpose and discourages those that do not.
To organize, one must connect people with each other in meaningful and purposeful ways. Further, a leader must connect people—human resources—with the information and technology necessary for them to be successful. Organizational structure defines the formal relationships among people and specifies both their roles and their responsibilities. Administrative systems govern the organization through guidelines, procedures, and policies. Information and technology define the process(es) through which members achieve outcomes. Each element must support each of the others, and together they must support the organization’s purpose, as reflected in its mission and vision.
For example, in 2006, Disney acquired Pixar, a firm renowned for its creative prowess in animated entertainment. Disney summarizes the Pixar strategy like this: “Pixar’s [strategy] is to combine proprietary technology and world-class creative talent to develop computer-animated feature films with memorable characters and heartwarming stories that appeal to audiences of all ages (Pixar, 2008).” Disney helped Pixar achieve this strategy through an important combination of structural design choices. First, Pixar is an independent division of Disney and is empowered to make independent choices in all aspects of idea development. Second, Pixar gives its “creatives”—its artists, writers, and designers—great leeway over decision-making. Third, Pixar protects its creatives’ ability to share work in progress, up and down the hierarchy, with the aim of getting it even better. Finally, after each project, teams conduct “postmortems” to catalog what went right and what went wrong. This way, innovations gained through new projects can be shared with later projects while at the same time-sharing knowledge about potential pitfalls (Catmull, 2008).
Organizational culture is the workplace environment formulated from the interaction of the employees in the workplace. Organizational culture is defined by all of the life experiences, strengths, weaknesses, education, upbringing, and other attributes of the employees. While executive leaders play a large role in defining organizational culture by their actions and leadership, all employees contribute to the organizational culture.
Achieving alignment between mission and vision and organizational culture can be very powerful, but culture is also difficult to change. This means that if an organization is seeking to change its vision or mission, a leader’s ability to change the organization’s culture to support those new directions may be difficult or, at least, slow to achieve.
For instance, in 2000, Procter & Gamble (P&G) sought to change a fundamental part of its vision in a way that asked the organization to source more of its innovations from external partners. Historically, P&G had invested heavily in research and development and internal sources of innovation—so much so that “not invented here” (known informally as NIH) was the dominant cultural mindset (Lafley & Charan, 2008). NIH describes a sociological, corporate, or institutional culture that avoids using products, research, or knowledge that originated anywhere other than inside the organization. It is normally used in a pejorative sense. As a sociological phenomenon, the “not invented here” syndrome is manifested as an unwillingness to adopt an idea or product because it originates from another culture. P&G has been able to combat this NIH bias and gradually change its culture toward one that is more open to external contributions and hence in much better alignment with its current mission and vision.
Social networks are often referred to as the “invisible organization.” They consist of individuals or organizations connected by one or more specific types of interdependencies. Most individuals are active in social network communities: Facebook, Instagram, LinkedIn, Reddit, and TikTok. However, these sites are only the tip of the iceberg when it comes to the emerging body of knowledge surrounding social networks. Networks deliver three unique advantages: access to “private” information (i.e., information that companies do not want competitors to have), access to diverse skill sets, and power. You may be surprised to learn that many big companies have breakdowns in communications, even in divisions where the work on one project should be related to work on another. Going back to our Pixar example, for instance, Disney is fostering a network among members of its Pixar division in a way that they are more likely to share information and learn from others. The open internal network also means that a cartoon designer might have easier access to a computer programmer, and together they can figure out a more innovative solution. Finally, since Pixar promotes communication across hierarchical levels and gives creatives decision-making authority, the typical power plays that might impede sharing innovation and individual creativity are prevented. Managers see these three network advantages at work every day but might not pause to consider how their networks regulate them.
Mission, Vision, and Leading
Leading involves influencing others toward the attainment of organizational objectives. Leading and leadership are nearly synonymous with the notions of mission and vision. We might describe a very purposeful person as being “on a mission.” As an example, Steve Demos had the personal mission of replacing cow’s milk with soymilk in U.S. supermarkets, and this mission led to his vision for and strategy behind, the firm White Wave and its Silk line of soymilk products (Carpenter & Sanders, 2006). Similarly, we typically think of some individuals as leaders because they are visionary. For instance, when Walt Disney suggested building a theme park in a Florida swamp back in the early 1960s, few other people in the world seemed to share his view.
Any task—whether launching Silk or building the Disney empire— is that much more difficult if attempted alone. Therefore, the more that a mission or vision challenges the status quo—and recognizing that good vision statements always need to create some dissonance with the status quo—the greater will the organization’s need be for what leadership researcher Shiba calls “real change leaders”—people who will help diffuse the revolutionary philosophy even while the leader (i.e., the founder or CEO) is not present. Without real change leaders, a revolutionary vision would remain a mere idea of the visionary CEO—they are the ones who make the implementation of the transformation real.
In most cases where we think of revolutionary companies, we associate the organization’s vision with its leader—for instance, Apple and Steve Jobs, Dell and Michael Dell, or Google with the team of Sergey Brin and Larry Page. Most importantly, in all three of these organizations, the leaders focused on creating an organization with a noble mission that enabled the employees and management team to achieve not only the strategic breakthrough but to also realize their personal dreams in the process. Speaking to the larger relationship between mission, vision, strategy, and leadership are the Eight principles of visionary leadership, derived from Shiba’s 2001 book, Four Practical Revolutions in Management (summarized in “Eight Principles of Visionary Leadership”) (Shiba & Walden, 2001).
Eight Principles of Visionary Leadership
- Principle 1 : The visionary leader must do on-site observation leading to personal perception of changes in societal values from an outsider’s point of view.
- Principle 2 : Even though there is resistance, never give up ; squeeze the resistance between outside-in (i.e., customer or society-led) pressure in combination with top-down inside instruction.
- Principle 3 : Revolution begins with symbolic disruption of the old or traditional system through top-down efforts to create chaos within the organization.
- Principle 4 : The direction of revolution is illustrated by a symbolically visible image and the visionary leader’s symbolic behavior .
- Principle 5 : Quickly establishing new physical, organizational, and behavioral systems is essential for a successful revolution.
- Principle 6 : Real change leaders are necessary to enable revolution.
- Principle 7 : Create an innovative system to provide feedback from results.
- Principle 8 : Create a daily operation system, including a new work structure, new approach to human capabilities and improvement activities .
Vision That Pervades the Organization
A broader definition of visionary leadership suggests that if many or most of an organization’s employees understand and identify with the mission and vision, efficiency will increase because the organization’s members “on the front lines” will be making decisions fully aligned with the organization’s goals. Efficiency is achieved with limited hands-on supervision because the mission and vision serve as a form of cruise control. To make frontline responsibility effective, leadership must learn to trust workers and give them sufficient opportunities to develop quality decision-making skills.
The classic case of Johnsonville Sausage, recounted by CEO Ralph Stayer, documents how how the company dramatically improved its fortunes after Stayer shared responsibility for the mission and vision and, ultimately, development of the actual strategy, with all of his employees. His vision was the quest for an answer to “What Johnsonville would have to be to sell the most expensive sausage in the industry and still have the biggest market share?" (Stayer, 1990). Of course, Stayer made other important changes as well, such as decentralizing decision-making and tying individual rewards to company-wide performance, but he initiated them by communicating the organization’s mission and vision and letting his employees know that he believed they could make the choices and decisions needed to realize them.
Mission and vision are also relevant to leadership well beyond the impact of one or several top executives. Even beyond existing employees, various stakeholders—customers, suppliers, and prospective new employees—are visiting organizations’ Web sites to read their mission and vision statements. In the process, they are trying to understand what kind of organization they are reading about and what the organization’s values and ethics are. Ultimately, they are seeking to determine whether the organization and what it stands for are a good fit for them.
Vision, Mission, and Controlling
Controlling involves ensuring that performance does not deviate from standards. Controlling consists of three steps: (1) establishing performance standards, (2) comparing actual performance against standards, and (3) taking corrective action when necessary. Mission and vision are both directly and indirectly related to all three steps.
Performance Standards
Recall that mission and vision tell a story about an organization’s purpose and aspirations. Mission and vision statements are often ambiguous by design because they are intended to inform the strategy, not be the strategy. Nevertheless, those statements typically provide a general compass heading for the organization and its employees. For instance, vision may say something about innovation, growth, or firm performance, and the firm will likely have set measurable objectives related to these. Performance standards often exceed actual performance; but ideally, managers will outline a set of metrics that can help to predict the future, not just evaluate the past.
It is helpful to think about such metrics as leading, lagging, and pacing indicators. A leading indicator actually serves to predict where the firm is going in terms of performance. For instance, General Electric asks customers whether they will refer it new business, and GE’s managers have found that this measure of customer satisfaction does a pretty good job of predicting future sales. A pacing indicator tells, in real time, that the organization is on track, for example, in on-time deliveries or machinery that is in operation (as opposed to being under repair or in maintenance). A lagging indicator is the one we are all most familiar with. Firm financial performance, for instance, is an accounting-based summary of how well the firm has done historically. Even if managers can calculate such performance quickly, the information is still historic and not pacing or leading. Increasingly, firms compile a set of such leading, lagging, and pacing goals and objectives and organize them in the form of a dashboard or Balanced Scorecard.
Actual Versus Desired Performance
The goals and objectives that flow from the mission and vision provide a basis for assessing actual versus desired performance. In many ways, such goals and objectives provide a natural feedback loop that helps managers see when and how they are succeeding and where they might need to take corrective action. This is one reason goals and objectives should ideally be specific and measurable. Moreover, to the extent that they serve as leading, lagging, and pacing performance metrics, they enable managers to take corrective action on any deviations from goals before too much damage has been done.
Corrective Action
Finally, just as mission and vision should lead to specific and measurable goals and objectives and thus provide a basis for comparing actual and desired performance, corrective action should also be prompted in cases where performance deviates negatively from performance objectives. It is important to point out that while mission and vision may signal the need for corrective action because they are rather general, high-level statements, they typically will not spell out specific actions—that latter part is the role of strategy, and mission and vision are critical for good strategies but not substitutes for them. A mission and vision are statements of self-worth. Their purpose is not only to motivate employees to take meaningful action but also to give leadership a standard for monitoring progress. It also tells external audiences how an organization wishes to be viewed and have its progress and successes gauged.
Strategic human resources management (SHRM) reflects the aim of integrating the organization’s human capital—its people—into the mission and vision. Human resources management alignment means to integrate decisions about people with decisions about the results an organization is trying to obtain. Research indicates that organizations that successfully align human resources management with mission and vision accomplishment do so by integrating SHRM into the planning process, emphasizing human resources activities that support mission goals, and building strong human resources/management capabilities and relationships (Gerhart & Rynes, 2003).
Key Takeaway
In addition to being a key part of the planning process, mission and vision also play key roles in the organizing, leading, and controlling functions of management. While mission and vision start the planning function, they are best realized when accounted for across all four functions of management—P-O-L-C. In planning, mission and vision help to generate specific goals and objectives and to develop the strategy for achieving them. Mission and vision guide choices about organizing, too, from structure to organizational culture. The cultural dimension is one reason mission and vision are most effective when they pervade the leadership of the entire organization rather than being just the focus of senior management.
Finally, mission and vision are tied to the three key steps of controlling:
- Establishing performance standards
- Comparing actual performance against standards
- Taking corrective action when necessary
Since people make the place, ultimately, strategic human resources management must bring these pieces together.
Exercises
- How might mission and vision influence organizational design?
- How might mission and vision influence leadership practices?
- Why might a specific replacement CEO candidate be a good or poor choice for a firm with an existing mission and vision?
- Which aspects of controlling do mission and vision influence?
- Why are mission and vision relevant to the management of internal organizational social networks?
- What performance standards might reinforce a firm’s mission and vision?
- What is the role of mission and vision for strategic human resource management?
Learning Objectives
- Understand how creativity relates to vision.
- Develop some creativity tools.
- Understand how passion relates to vision.
Creativity and passion are particularly relevant to a company's mission and vision statements. A simple definition of creativity is the power or ability to invent.  Passion, at least in the context we invoke here, refers to an intense, driving, or overmastering feeling or conviction. Passion is also associated with intense emotion that compels action. We will focus mostly on the relationship between creativity, passion, and vision in this section because organizational visions are intended to create uneasiness with the status quo and help inform and motivate key stakeholders to move the organization forward. This means that a vision statement should reflect and communicate something that is relatively novel and unique, and such novelty and uniqueness are the products of creativity and passion.
Creativity and passion can, and probably should, also influence the organization’s mission. In many ways, the linkages might be clearest between creativity and vision statements and passion and mission statements because the latter is an expression of the organization’s values and deeply held beliefs. Similarly, while we will discuss creativity and passion separately in this section, your intuition and experience surely tell you that creativity eventually involves emotion, to be creative, to care about—be passionate about—what one is doing.
Creativity and Vision
Work by DeGraf and Lawrence (2022) suggests a finer-grained view into the characteristics and types of creativity. They argued that creativity “types” could be clustered based on some combination of flexibility versus control and internal versus external orientation. For the manager, their typology is especially useful as it suggests ways to manage creativity, as in simply hiring creative individuals. As summarized in the figure, their research suggests that there are four types of creativity:
- Investment (external orientation with high control)
- Imagination (external orientation with flexibility emphasis)
- Improvement (internal orientation with high control)
- Incubation (internal orientation with flexibility emphasis).
The first type of creativity, investment , is associated with speed—being first and being fast. It is also a form of creativity fostered from the desire to be highly competitive. Perhaps one of the most recent examples of this type of creativity crucible is the beer wars—the battle for U.S. market share between SABMiller PLC and Anheuser Busch (AB; Budweiser). Miller was relentless in attacking the quality of AB’s products through its advertisements and at the same time launched myriad new products to take business from AB’s stronghold markets (Biz Journals, 2008).
The second type of creativity, imagination , is the form that many think of first. This type of creativity is characterized by new ideas and breakthroughs: Apple’s stylish design of Macintosh computers and then game-changing breakthroughs with its iPod and iPhone. Oftentimes, the drive to tie this type of creativity can result in the genius of a single individual, such as Apple’s Steve Jobs .
Where big ideas come from the imagination quadrant, improvement is a type of creativity that involves making an existing idea better. Two great examples of this are McDonald’s and Toyota. Ray Kroc, McDonald’s founder, had the idea of creating quality and cooking standards for preparing tasty burgers and fries. While there were many other burger joints around at the time (the 1950s), Kroc’s unique process-oriented approach gave McDonald’s a big advantage. Similarly, Toyota has used the refinement of its auto making and auto-assembly processes (called the Toyota Business System) to be one of the largest and most successful, high-quality car makers in the world.
Finally, the fourth area of creativity is incubation . Incubation is a very deliberate approach that concerns a vision of sustainability—that is, leaving a legacy. This type of creativity is more complex because it involves teamwork, empowerment, and collective action. In their chapter on problem-solving, David Whetten and Kim Cameron provide Gandhi as an example of incubation creativity:
“Mahatma Gandhi was probably the only person in modern history who has single-handedly stopped a war. Lone individuals have started wars, but Gandhi was creative enough to stop one. He did so by mobilizing networks of people to pursue a clear vision and set of values. Gandhi would probably have been completely noncreative and ineffective had he not been adept at capitalizing on incubation dynamics. By mobilizing people to march to the sea to make salt, or to burn passes that demarcated ethnic group status, Gandhi was able to engender creative outcomes that had not been considered possible. He was a master at incubation by connecting, involving, and coordinating people" (Whetten & Camerson, 2007).
While no one of these four types of creativity is best, they have some contradictory or conflicting characteristics. For example, imagination and improvement emphasize different approaches to creativity. The size of the new idea, for instance, is typically much bigger with imagination (i.e., revolutionary solutions) than with improvement (i.e., incremental solutions). Investment and incubation also are very different; investment is relatively fast and the other relatively slow (i.e., incubation emphasizes deliberation and development).
Creativity Tools
In this section, we introduce two creativity tools: SCAMPER and the Nominal Group Technique . This set of tools is not exhaustive but provides good intuition and resources to develop new ideas—either to craft a vision for a new company or revise an existing mission and vision. The first three tools can be used and applied individually or in groups; Nominal Group Technique is designed to bolster creativity in groups and can build on individual and group insights provided by the other tools.
All these tools help you to manage two divergent forms of thinking necessary for creativity—programmed thinking and lateral thinking. Programmed thinking, often called left-brained thinking, relies on logical or structured ways of creating a new product or service. In terms of mission and vision, this means a logical and deliberate process is used to develop the vision statement. Lateral thinking a term coined by Edward DeBono in his book The Use of Lateral Thinking (1967), is about changing patterns and perceptions; it is about ideas that may not be obtainable by using only traditional step-by-step, programmed logic (De Bono, 1992). Lateral thinking draws on the right side of our brains.
Each type of approach—programmed versus lateral—has its strength. Programmed thinking, which is logical and disciplined, is enormously effective in making products and services better. It can, however, only go so far before all practical improvements have been carried out. Lateral thinking can generate completely new concepts and ideas and brilliant improvements to existing systems. In the wrong place, however, it can be impractical or unnecessarily disruptive.
SCAMPER
Developed by Bob Eberle, SCAMPER is a checklist tool that helps you to think of changes you can make to an existing marketplace to create a new one—a new product, a new service, or both (Eberle, 1997). You can use these changes either as direct suggestions or as starting points for lateral thinking. This, in turn, can inspire a new vision statement. Table 8.1, “Creativity through SCAMPER,” provides you with the SCAMPER question steps and examples of new products or services that you might create.
| Questions: | Examples: |
|---|---|
| Substitute : What else instead? Who else instead? Other ingredients? Other material? Other time? Other place? | Vegetarian hot dogs |
| Combine : How about a blend? Combine purposes? Combine materials? | Musical greeting cards |
| Adapt : What else is like this? What other idea does this suggest? How can I adjust to these circumstances? | Snow tires |
| Modify : Different order, form, shape? Minify : What to make smaller? Slower? Lighter? What to do with less frequency? Magnify : What to make higher? Longer? Thicker? What to do with greater frequency? | Scented crayons; Bite-sized Snickers bars; Super-sized french fries |
| Put to other uses : New ways to use as is? Other uses I modified? Other places to use an item or movement? | Towel as fly swatter |
| Eliminate : What to remove? Omit? Understate? | Cordless telephone |
| Rearrange : Other layout? Other sequence? Transpose cause and effect? Transpose positive and negative? How about opposites? Reverse : Interchange components? Other pattern? Backward? Upside down? | Vertical stapler; Reversible clothing |
As shown in Table 8.1, by taking a topic or problem and then using SCAMPER, you can generate possible new products. It may be some combination of these SCAMPER changes that lead to highly innovative solutions. For instance, the entertainment company Cirque du Soliel has modeled its shows on the traditional circus. However, it has adapted aspects of theater and opera, eliminated animals, and reduced the number of rings from three to one. As a result, it offers a highly stylized (and much more expensive!) version of what, nostalgically, we call a circus today. Many of the ideas may be impractical. However, some of these ideas could be good starting points for a new organization or revision of the vision for an existing one.
Nominal Group Technique
The Nominal Group Technique (NGT) is a method of facilitating a group of people to produce a large number of ideas in a relatively short time (University of Wisconsin Extension Program, 2008). In addition to using NGT to develop a mission and vision statement, it can be useful:
- To generate numerous creative ideas
- To ensure everyone is heard
- When there is concern that some people may not be vocal
- To build consensus
- When there is controversy or conflict
As shown in “NGT Preparation and Supplies,” preparation and supplies are modest. It encourages contributions from everyone by allowing for equal participation among group members. A question is posed to the group. Individually and silently, each participant writes down his or her ideas. In round-robin fashion, each member supplies an idea until all ideas are shared. Generally, 6 to 10 people participate. “Nominal” means that the participants form a group in name only. For most of the session, they do not interact as they would in other group processes.
NGT Preparation and Supplies
Formulate your discussion question. Ensure that the wording prevents misunderstanding and is objective. Supplies needed include:
- Flip chart for each table
- Masking tape
- 3 × 5 cards for each participant
- Work tables
- Pens or markers
The group is divided into small work groups, each with a leader. A flip chart and markers are needed at each table. Position the flip chart so that all can see the ideas. The remaining simple procedures are summarized in the following NGT Procedure.
NGT Procedure
- Introduction: Briefly welcome participants, clarify the purpose of the group exercise, and explain the procedure to be followed and how results are to be used.
- Present question: Orally present the question that is written on the flip chart; clarify as needed.
- Silent generation of ideas: Each participant silently thinks of and writes down (on a 3×5 card) as many ideas as possible. Allow 5 to 10 minutes.
- Record ideas: In turn, each participant reads aloud one idea, and it is recorded on the flip chart for all to see.
- Continue until all ideas are recorded.
- Discourage discussion, not even questions for clarification.
- Encourage “hitchhiking,” that is, expanding on another’s statement. Ideas do not have to be from the participant’s written list.
- Participants may pass a turn and then add an idea at a subsequent turn.
- Discourage combining ideas from individuals unless they are exactly the same.
- Group discussion: After all ideas are recorded, the person who suggested the idea is given the opportunity to explain it further.
- Duplicates may be combined.
- Wording may be changed if the originator agrees.
- Ideas are deleted only by unanimous agreement.
- Restrict discussion to clarify meaning; the value or merit of ideas is not discussed.
Passion and Vision
Passion as we invoke the term in this chapter, refers to intense, driving, or overmastering feeling or conviction. Passion is also associated with intense emotion that compels action. Passion is relevant to vision in at least two ways: (1) Passion about an idea as inspiration of the vision and vision statement and (2) shared passion among organizational members about the importance of the vision.
Passion as Inspiration
Entrepreneur Curt Rosengren makes this observation about the relationship between passion and entrepreneurship: “Strangely, in spite of its clear importance, very few entrepreneurs or managers consciously incorporate passion into their decisions, ultimately leaving one of their most valuable assets on their path to success largely to chance, even though there is little question that passion can be a part of vision creation" (Astroprojects, 2008). Rosengren comments further that:
Passion is the essence of the entrepreneurial spirit. It is an entrepreneur’s fuel, providing the drive and inspiration to create something out of nothing while enduring all the risks, uncertainty, and bumps in the road that that entails. Entrepreneurs’ lives consist of a nonstop mission to communicate their vision and inspire others to support their efforts. As evangelists, salespeople, fundraisers, and cheerleaders they need to breathe life into their vision while enlisting others in their dream. From creating a vision for the future to selling the idea to investors, from attracting high-quality employees to inspiring them to do what nobody thought possible, that passion is a key ingredient. Passion also plays a key role in their belief that they can achieve the so-called impossible, bouncing back from failure and ignoring the chorus of No that is inevitably part of the entrepreneurial experience. Robin Wolaner, founder of Parenting magazine and author of Naked In The Boardroom: A CEO Bares Her Secrets So You Can Transform Your Career, put it succinctly when she said, ‘To succeed in starting a business you have to suspend disbelief, because the odds are against you. Logic is going to stop you.’ Passion, on the other hand, will help you fly. (Astroprojects, 2008)
Passion About the Vision
Passion doesn’t just have benefits for the individual entrepreneur or manager when formulating a vision statement, it can help the whole business thrive. While there is little academic research on the relationship between passion and vision, studies suggest that fostering engagement, a concept related to passion, in employees has a significant effect on the corporate bottom line. Gallup , for instance, has been on the forefront of measuring the effect of what it calls employee engagement. Employee engagement is a concept that is generally viewed as managing discretionary effort; that is, when employees have choices, they will act in a way that furthers their organization’s interests. An engaged employee is fully involved in, and enthusiastic about, his or her work (Gallup, 2008). The consulting firm, Blessing/White, Inc., offers this description of engagement and its value (and clear relationship with passion):
“Engaged employees are not just committed. They are not just passionate or proud. They have a line-of-sight on their own future and on the organization’s mission and goals. They are ‘enthused’ and ‘in gear’ using their talents and discretionary effort to make a difference in their employer’s quest for sustainable business success" (BlessingWhite, 2008).
Engaged employees are those who are performing at the top of their abilities and are happy about it. According to statistics that Gallup has drawn from 300,000 companies in its database, 75%–80% of employees are either “disengaged” or “actively disengaged" (Gallup, 2008).
That’s an enormous waste of potential. Consider Gallup’s estimation of the impact if 100% of an organization’s employees were fully engaged:
- Customers would be 70% more loyal.
- Turnover would drop by 70%.
- Profits would jump by 40%.
Job satisfaction studies in the United States routinely show job satisfaction ratings of 50%–60%. But one recent study by Harris Interactive of nearly 8,000 American workers went a step further (Zinkewicz, 2005). What did the researchers find?
- Only 20% feel very passionate about their jobs.
- Less than 15% agree that they feel strongly energized by their work.
- Only 31% (strongly or moderately) believe that their employer inspires the best in them.
Consciously creating an environment where passion is both encouraged and actively developed can yield an enormous competitive advantage. That environment starts at the top through the development and active communication of mission and vision.
Key Takeaway
You learned about the relationship between creativity and passion and mission and vision. You learned that creativity relates to the power or ability to create and that passion is intense emotion that compels action. Creativity is important if the desired mission and vision are desired to be novel and entrepreneurial; passion is important both from the standpoint of adding energy to the mission and vision and to key stakeholders following the mission and vision.
Exercises
- What is creativity?
- Why is creativity relevant to vision and vision statements?
- What are some useful creativity tools?
- What is passion?
- Why is passion relevant to vision and vision statements?
- What is the relationship between passion and engagement?
Learning Objectives
- Learn about stakeholders and their importance.
- Understand stakeholder analysis.
- Be able to map stakeholders and their level of participation.
Learning Objectives
- Learn about the basics of the mission and vision development process.
- Understand the content of good mission and vision statements.
Communicating and Monitoring Mission and Vision
At this point, you have an understanding of what a mission and vision statement is and how creativity, passion, and stakeholder interests might be accounted for. The actual step-by-step process of developing a mission and vision might start with the mission and vision statements, but you should think of this process more broadly in terms of multiple steps: (1) the process, (2) the content of the mission and vision statements, (3) communicating mission and vision to all relevant stakeholders, and (4) monitoring. As shown in “Process, Content, Application, and Monitoring in Mission and Vision Development,” Information Week breaks out one way you might manage your mission/vision development checklist. Let’s dive into the development process first (InformationWeek Staff, 2004).
Mission and vision statements are statements of an organization’s purpose and potential: what you want the organization to become. Both statements should be meaningful to you and your organization. It should be shared with all of the employees in the organization to create a unified direction for everyone to move in.
Process, Content, Application, and Monitoring in Mission and Vision Development
- Let the business drive the mission and vision .
- Involve all stakeholders in its development; otherwise, they won’t consider it theirs.
- Assign responsibility so that it’s clear how each person, including each stakeholder, can contribute.
- Seek expert facilitation to reach a vision supported by all.
- Revise and reiterate; you’ll likely go through multiple iterations before you’re satisfied.
- Start from where you are to get to where you want to go.
- Build in the values of the organization : Every organization has a soul. Tap into yours, and adjust as needed. Mission and vision built on your values will not just hold promise but also deliver on it.
- Build on the core competencies of the organization : A mission and vision are useless if they can’t be put into operation. This requires recognition of your organization’s strengths and weaknesses.
- Factor in your style : A mission and vision must reflect the leader’s style. You can’t sustain action that goes against it.
- Make it visual : A picture is worth a thousand words.
- Make it simple to understand : Complex language and disconnected statements have little impact—people can’t implement what they don’t understand.
- Make it achievable : A mission and vision are an organization’s dreams for the future. Unachievable goals discourage people.
- Phase it in : Reach for the sky—in stages.
- Make it actionable : If it’s too abstract, no one knows what to do next.
- Communicate often : Internal communications are the key to success. People need to see the mission and vision, identify with them, and know that leadership is serious about it.
- Create messages that relate to the audience : To adopt a mission and vision, people must see how they can achieve it and what’s in it for them.
- Create messages that inspire action : It’s not what you say but how you say it.
- Use it : Beyond printing it, posting it, and preaching it, you also must practice what is laid out in the mission and vision—in other words, “walk the talk.”
- Live it : Management must lead by example.
- Be real : It’s better to adjust the mission statement as needed than to not live up to the standards it sets.
- Identify key milestones : While traveling to your destination, acknowledge the milestones along the way.
- Monitor your progress : A strategic audit, combined with key metrics, can be used to measure progress against goals and objectives.
- Use an external audit team : An external team brings objectivity, plus a fresh perspective.
Mission and Vision-Development Process
Mission and vision development are analogous to the “P” (planning) in the P-O-L-C framework. Start with the people. To the greatest extent possible, let those people responsible for executing the mission and vision drive their development. Sometimes this means soliciting their input and guiding them through the development of the actual statements, but ideally, it means teaching them how to craft those statements themselves. Involve as many key stakeholders as possible in its development; otherwise, they won’t consider it theirs. Assign responsibility so that it’s clear how each person, including each stakeholder, can contribute.
Content
The content of the mission and vision statements are analogous to the O (organizing) part of the P-O-L-C framework. Begin by describing the best possible business future for your company, using a target of 5 to 10 years in the future. Your written goals should be dreams, but they should be achievable dreams. Jim Collins (author of Good to Great ) suggests that the vision be very bold, or what he likes to call a BHAG—a big, hairy, audacious goal—like the United States' goal in the 1960s to go to the moon by the end of the decade, or Martin Luther King’s vision for a nonracist America.
Recognizing that the vision statement is derived from aspects of the mission statement, it is helpful to start there. Richard O’Hallaron and his son, David R. O’Hallaron, in The Mission Primer: Four Steps to an Effective Mission Statement , suggest that you consider a range of objectives, both financial and non-financial (O’Hallaron & O’Hallaron, 2000). Specifically, the O’Hallarons find that the best mission statements have given attention to the following six areas:
- What “want-satisfying” service or commodity do we produce and work constantly to improve?
- How do we increase the wealth or quality of life or society?
- How do we provide opportunities for the productive employment of people?
- How are we creating a high-quality and meaningful work experience for employees?
- How do we live up to the obligation to provide fair and just wages?
- How do we fulfill the obligation to provide a fair and just return on capital?
When writing statements:
- Use the present tense, speaking as if the business has already become what you are describing
- Use descriptive statements describing what the business looks like and feels like, using words that describe all of a person’s senses
- Your words will be a clear written motivation for where your business organization is headed.
- Mission statements, because they cover more ground, tend to be longer than vision statements. However, aim to write no more than a page.
- Your words can be as long as you would like them to be, but a shorter vision statement will be easier to remember.
Communications
The communications step of the mission and vision statements development process is analogous to the “L” (leading) part of the P-O-L-C framework. Communicate often: Internal communications are the key to success. People need to see the vision, identify with it, and know that leadership is serious about it.
Managers must evaluate both the need and the necessary tactics for persuasively communicating a strategy in four different directions: upward , downward , across , and outward (Hambrick & Cannella, 1989).
Communicating Upward
Increasingly, firms rely on bottom-up innovation processes that encourage and empower middle-level and division managers to take ownership of mission and vision and propose new strategies to achieve them. Communicating upward means that someone or some group has championed the vision internally and has succeeded in convincing top management of its merits and feasibility.
Communicating Downward
Communicating downward means enlisting the support of the people who will be needed to implement the mission and vision. Too often, managers undertake this task only after a strategy has been set in stone, thereby running the risk of undermining both the strategy and any culture of trust and cooperation that may have existed previously. Starting the communication process early is the best way to identify and surmount obstacles, and it usually ensures that a management team is working with a common purpose and intensity that will be important when it’s time to implement the strategy.
Communicating Across and Outward
The need to communicate across and outward reflects the fact that the realization of a mission and vision will probably require cooperation from other units of the firm ( across ) and from key external stakeholders, such as material and capital providers, complementors, and customers ( outward ). Internally, for example, the strategy may call for raw materials or services to be provided by another subsidiary; perhaps it depends on sales leads from other units. The software company Emageon couldn’t get hospitals to adopt the leading-edge visualization software that was produced and sold by one subsidiary until its hardware division started cross-selling the software as well. This internal coordination required a champion from the software side to convince managers on the hardware side of the need and benefits of working together.
Application
It is the successful execution of this step—using the mission and vision statements—that eludes most organizations. “Yes, it is inconvenient and expensive to move beyond the easy path” and make decisions that support the mission statement, says Lila Booth, a Philadelphia-area consultant who is on the faculty of the Wharton Small Business Development Center. But ditching mission for expediency “is short-term thinking,” she adds, “which can be costly in the end, costly enough to put a company out of business" (Krattenmaker, 2002). That is not to say that a mission statement is written in stone. Booth cites her own consulting business. It began well before merger mania but has evolved with the times and now is dedicated in significant part to helping merged companies create common cultures. “Today, our original mission statement would be very limiting,” she says.
Even the most enthusiastic proponents acknowledge that mission statements are often viewed cynically by organizations and their constituents. That is usually due to large and obvious gaps between a company’s words and deeds. “Are there companies that have managers who do the opposite of what their mission statements dictate? Of course,” says Geoffrey Abrahams, author of The Mission Statement Book . “Mission statements are tools, and tools can be used or abused or ignored.…Management must lead by example. It’s the only way employees can live up to the company’s mission statement" (Abrahams, 1999).
Ultimately, if you are not committed to using the mission statement, then do not create one.
Monitoring
The monitoring step of the mission and vision statements development process is analogous to the “C” (controlling) part of the P-O-L-C framework. Identify key milestones that are implied or explicit in the mission and vision. Since mission and vision act like a compass for a long trip to a new land, as Information Week suggests, “while traveling to your destination, acknowledge the milestones along the way. With these milestones, you can monitor your progress: A strategic audit, combined with key metrics, can be used to measure progress against goals and objectives. To keep the process moving, try using an external audit team. One benefit is that an external team brings objectivity, plus a fresh perspective" (InformationWeek Staff, 2004). It also helps motivate your team to stay on track.
Key Takeaway
This section described some of the basic inputs into crafting mission and vision statements. It explored how mission and vision involved initiation, determination of content, communication, application, and then monitoring to be sure if and how the mission and vision were being followed and realized. In many ways, you learned how the development of mission and vision mirrors the P-O-L-C framework itself—from planning to control (monitoring).
Exercises
- Who should be involved in the mission and vision development process?
- What are some key content areas for mission and vision?
- Why are organizational values important to mission and vision?
- Why is communication important with mission and vision?
- To which stakeholders should the mission and vision be communicated?
- What role does monitoring play in mission and vision?
Learning Objectives
- Determine what mission and vision mean for you.
- Develop some guidelines for developing your mission and vision.
Mission and vision are concepts that can be applied to you, personally, well beyond their broader relevance to the P-O-L-C framework. Personal mission and vision communicate the direction in which you are headed, as well as providing some explanation for why you are choosing one direction or set of objectives over others. Thinking about and writing down mission and vision statements for your life can help provide you with a compass as you work toward your own goals and objectives.
Your Mission and Vision
Note that the development of a personal mission and vision, and then a strategy for achieving them, are exactly the opposite of what most people follow. Most people do not plan further ahead than their next job or activity (if they plan their career at all). They take a job because it looks attractive, and then they see what they can do with it. We advocate looking as far into the future as you can and deciding where you want to end up and what steps will lead you there.
Guidelines
The first step in planning a career is obviously a long-term goal. Where do you want to end up, ultimately? Do you really want to be a CEO or president of the United States, now that you know what it costs to be either one? There are a couple basic parts to this process.
BHAG
First, set out a bold vision—Jim Collins, author of Good to Great , describes this as a BHAG a b ig, h airy, a udacious g oal .
Five guiding criteria for good BHAGs is that they:
- Are set with understanding, not bravado.
- Fit squarely in the three circles of (a) what you are deeply passionate about (including your core values and purpose), (b) what drives your economic logic, and (c) what differentiates you (what you can be the best in the world at).
- Have a long time frame—10 to 30 years.
- Are clear, compelling, and easy to grasp.
- Directly reflect your core values and core purpose.
Values
Second, sketch out your personal values, or “Guiding Philosophy”—a set of core values and principles like your own Declaration of Independence.
Schedule
Once the vision is set, you have to develop some long-term goal (or goals), then intermediate-term goals, and so on. If you want to be President, what jobs will you have to take first to get there, and when do you have to get these jobs? Where should you live? What training do you need? What political connections do you need? Then you have to set up an orderly plan for obtaining the connections and training that you need and getting into these steppingstone jobs.
Finally, you need to establish short-term goals to fit clearly into a coherent plan for your entire career. Your next job (if you are now a fairly young person) should be picked not only for its salary or for its opportunities for advancement but for its chances to provide you with the training and connections you need to reach your long-term goals. The job that is superficially attractive to you because it has a high salary, offers the opportunity for immediate advancement, or is located in a desirable place may be a mistake from the standpoint of your long-term career.
Five Steps
Former business school professor, entrepreneur (founder of www.quintcareers.com and now called: https://www.livecareer.com ), and colleague Randall S. Hansen, PhD, has done a masterful job of assembling resources that aim to help your career, including an excellent five-step plan for creating personal mission statements. With his generous permission, he has allowed us to reproduce his five-step plan—adapted by us to encompass both mission and vision—in this section.
The Five-Step Plan
A large percentage of companies, including most of the Fortune 500, have corporate mission and vision statements (Purpose Brand, 2021). Mission and vision statements are designed to provide direction and thrust to an organization, an enduring statement of purpose. A mission and vision statement acts as an invisible hand that guides the people in the organization. A mission and vision statement explains the organization’s reason for being and answers the question, “What business are we in?”
A personal mission and vision statement is a bit different from a company mission statement, but the fundamental principles are the same. Writing a personal mission and vision statement offers the opportunity to establish what’s important and perhaps make a decision to stick to it before we even start a career. Or it enables us to chart a new course when we’re at a career crossroads. Steven Covey (in First Things First ) refers to developing a mission and vision statement as “connecting with your own unique purpose and the profound satisfaction that comes from fulfilling it" (Covey, 1994).
A personal mission and vision statement helps job-seekers identify their core values and beliefs. Michael Goodman (in The Potato Chip Difference: How to Apply Leading Edge Marketing Strategies to Landing the Job You Want ) states that a personal mission statement is “an articulation of what you’re all about and what success looks like to you" (Goodman, 2001). A personal mission and vision statement also allows job seekers to identify companies that have similar values and beliefs and helps them better assess the costs and benefits of any new career opportunity.
The biggest problem most job seekers face is not in wanting to have a personal mission and vision statement but in writing it. So, to help you get started on your personal mission and vision statement, here is a five-step mission/vision-building process. Take as much time on each step as you need, and remember to dig deeply to develop a mission and vision statement that is both authentic and honest. To help you better see the process, Professor Hansen included an example of one friend’s process in developing her mission and vision statements.
Sample Personal Mission Statement Development
-
Past success
:
- developed new product features for stagnant product
- part of the team that developed a new positioning statement for product
- helped child’s school with fundraiser that was wildly successful
- increased turnout for the opening of a new local theater company
Themes: Successes all relate to creative problem-solving and execution of a solution.
-
Core values
:
- Hard-working
- Industrious
- Creativity
- Problem-solving
- Decision maker
- Friendly
- Outgoing
- Positive
- Family-oriented
- Honest
- Intelligent
- Compassionate
- Spiritual
- Analytical
- Passionate
- Contemplative
Most important values:
- Problem-solving
- Creativity (most important value!)
- Analytical
- Compassionate
- Decision maker
- Positive
-
Identify Contributions
:
- the world in general: develop products and services that help people achieve what they want in life. To have a lasting effect on the way people live their lives.
- my family: to be a leader in terms of personal outlook, compassion for others, and maintaining an ethical code; to be a good mother and a loving wife; to leave the world a better place for my children and their children.
- my employer or future employers: to lead by example and demonstrate how innovative and problem-solving products can be both successful in terms of solving a problem and successful in terms of profitability and revenue generation for the organization.
- my friends: to always have a helping hand for my friends, for them to know they can always come to me with any problem.
- my community: to use my talents in such a way as to give back to my community.
-
Identify Goals
:
Short-term: To continue my career with a progressive employer that allows me to use my skills, talent, and values to achieve success for the firm
Long-term: To develop other outlets for my talents and develop a longer-term plan for diversifying my life and achieving both professional and personal success
-
Mission Statement
:
To live life completely, honestly, and compassionately, with a healthy dose of realism mixed with the imagination and dreams that all things are possible if one sets their mind to finding an answer.
Vision Statement :
To be the CEO of a firm that I start, that provides educational exercise experiences to K–6 schools. My company will improve children’s health and fitness and create a lasting positive impact on their lives and those of their children.
Step 1: Identify Past Successes. Spend some time identifying four or five examples where you have had personal success in recent years. These successes could be at work, in your community, or at home. Write them down. Try to identify whether there is a common theme—or themes—to these examples. Write them down.
Step 2: Identify Core Values. Develop a list of attributes that you believe identify who you are and what your priorities are. The list can be as long as you need. Once your list is complete, see whether you can narrow your values to five or six most important values. Finally, see whether you can choose the one value that is most important to you. We’ve added “Generating Ideas for Your Mission and Vision” to help jog your memory and brainstorm about what you do well and really like to do.
Step 3: Identify Contributions. Make a list of the ways you could make a difference. In an ideal situation, how could you contribute best to:
- the world in general
- your family
- your employer or future employers
- your friends
- your community
Generating Ideas for Your Mission and Vision
A useful mission and vision statement should include two pieces: what you wish to accomplish and contribute and who you want to be, the character strengths and qualities you wish to develop. While this sounds simple, those pieces of information are not always obvious. Try these tools for generating valuable information about yourself.
Part I
- Describe your ideal day. This is not about being practical. It is designed to include as many sides of you and your enthusiasms as possible: creative, competent, artistic, introverted, extroverted, athletic, playful, nurturing, contemplative, and so on.
- Imagine yourself 132 years old and surrounded by your descendants or those descendants of your friends. You are in a warm and relaxed atmosphere (such as around a fireplace). What would you say to them about what is important in life? This exercise is designed to access the values and principles that guide your life.
- Imagine that it is your 70th birthday (or another milestone in your life). You have been asked by national print media to write a press release about your achievements. Consider what you would want your family, friends, and coworkers in your profession and in your community to say about you. What difference would you like to have made in their lives? How do you want to be remembered? This is designed to inventory your actions and accomplishments in all areas of your life.
Part II
Review your notes for these three exercises. With those responses in mind, reflect on questions 1, 2, and 3 above. Then write a rough draft (a page of any length) of your mission statement. Remember that it should describe what you want to do and who you want to be. This is not a job description. Carry it with you, post copies in visible places at home and work, and revise and evaluate. Be patient with yourself. The process is as important as the outcome. After a few weeks, write another draft. Ask yourself whether your statement was based on proven principles that you believe in and if you feel direction, motivation, and inspiration when you read it. Over time, reviewing and evaluating will keep you abreast of your own development.
Step 4: Identify Goals. Spend some time thinking about your priorities in life and the goals you have for yourself. Make a list of your personal goals, perhaps in the short term (up to three years) and the long term (beyond three years).
Step 5: Write Mission and Vision Statements. Based on the first four steps and a better understanding of yourself, begin writing your personal mission and vision statements.
Final thoughts: A personal mission and vision statement is, of course, personal. But if you want to see whether you have been honest in developing your personal mission and vision statement, we suggest sharing the results of this process with one or more people who are close to you. Ask for their feedback. Finally, remember that mission and vision statements are not meant to be written once and blasted into stone. You should set aside some time annually to review your career, job, goals, and mission and vision statements—and make adjustments as necessary.
Key Takeaway
In this section, you learned how to think of mission and vision in terms of your personal circumstances, whether it is your career or other aspects of your life. Just as you might do in developing an organization’s vision statement, you were encouraged to think of a big, hairy audacious goal (BHAG) as a starting point. You also learned a five-step process for developing a personal vision statement.
Exercises
- How does a personal mission and vision statement differ from one created for an organization?
- What time period should a personal mission and vision statement cover?
- What are the five steps for creating a personal mission and vision statement?
- What type of goals should you start thinking about in creating a personal mission and vision?
- How are your strengths and weaknesses relevant to mission and vision?
- What stakeholders seem relevant to your personal mission and vision?


Page 1.3: Rules of Exponents and Radicals
A big part of learning calculus involves being able to understand the notation that is used. More generally, anytime a new symbol is introduced, we should question it and see several examples and non-examples. Often, the purpose of a symbol is to provide a means of simplifying the notation and this is also the case when it comes to exponents and radicals. For instance, it would be rather cumbersome to write \( 5 \times 5 \times 5 \times 5 \) and even more cumbersome if we wished to multiply \(5\) by itself twenty times. Thus, we introduce the notion of an exponent . Instead of writing \( 5 \times 5 \times 5 \times 5 \), we can simply denote this as \( 5^4\) which is read as "\(5\) raised to the fourth power" and in the case of multiplying \(5\) by itself twenty times, rather than writing \( 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \), we may simply denote this by \(5^{20}\). We call \(5\) the base and we call \(20\) the exponent .
More generally, we make the following definition.
Definition: If \(a\) is any real number and \(n\) is any positive integer, then the \(n^{th} \) power of \(a\) is denoted by \( a^n \) where
\[ a^n = \underbrace{a \times a \times \ldots \times a}_{n ~ \text{times} } \]
The number \(a\) is called the base and \(n\) is called the exponent .
Whenever a definition is provided, we should reflect on the assumptions and requirements of the definition. Doing so will lead to us a deeper understanding of the material.
Here, we notice that the definition requires \(a\) to be a real number and pretty much all the numbers we will see in calculus will be real numbers (the main exception to this will be noted later on). Since most of the numbers we see will be real numbers, we will not place too much attention on \(a\). Rather, our focus is on \(n\). We see our definition requires \(n\) to be a positive integer . This immediately raises two questions:
- Is it possible for \(n\) to be negative? For instance, how do we define \(5^{-20} \)?
- Is it possible for \(n\) to not be an integer? For instance, what does \(5^{20.23} \) mean?
We will consider the answer to these two questions in just a moment. For now, allow us to consider some examples.
Compute the following:
1) \( \bigg(\dfrac{1}{2} \bigg)^5 \)
2) \(2^4 \)
3) \( (-2)^{4} \)
4) \( - 2^4 \)
5) \( (-2)^3 \)
6) \( - 2^3 \)
- Answer
-
1) \( (\frac{1}{2} )^5 = (\frac{1}{2}) \times (\frac{1}{2}) \times (\frac{1}{2}) \times (\frac{1}{2}) \times (\frac{1}{2}) = \frac{1}{32} \)
2) \(2^4 = (2)(2)(2)(2) = 16 \)
3) \( (-2)^4 = (-2)(-2)(-2)(-2) = 16 \)
4) \( - 2^4 = - (2)(2)(2)(2) = - 16 \)
5) \( (-2)^3 = (-2)(-2)(-2) = -8 \)
6) \( - 2^3 = - (2)(2)(2) = -8 \)
We now turn our attention to the first question posed earlier: is it possible for \(n\) to be negative? The answer is yes:
Definition: If \(a \neq 0\) is a real number and \(n\) is a positive integer, then
\[ a^{-n} = \dfrac{1}{a^n} ~~ \text{and}~~ a^0 = 1 \nonumber\ \]
As mentioned above, whenever a definition is provided, we should reflect on the assumptions and requirements of the definition. Doing so will lead to us a deeper understanding of the material. Here, we see that \(a\) is not allowed to be equal to zero and we may wonder why. That is, what does \( 0^0 \) equal to? The answer is that for us, \(0^0 \) is not defined! We will touch a little bit more upon this in Day 8 but for those who are interested, a good exercise is to graph the functions \( f(x) = x^0 \) and \(g(x) = 0^x \). What happens to the values of \(f\) and \(g\) as \(x\) gets closer and closer to zero from th right hand side? It is okay if we cannot answer this now since the solution will be apparent by Day 8. In the meantime, allow us to consider the following example.
Compute the following:
1) \( \bigg(\dfrac{1}{2} \bigg)^{-5} \)
2) \(2^{-4} \)
3) \( (-2)^{-4} \)
4) \( -2^{-4} \)
5) \( (-2)^{-3} \)
6) \( -2^{-3} \)
7) \( x^{-1} \) you may assume that \(x \neq 0 \).
8) \( x^{-2} \) you may assume that \(x \neq 0 \).
9) \( x^{-3} \) you may assume that \(x \neq 0 \).
10) \( x^{-2023} \) you may assume that \(x \neq 0 \).
11) \(2023^0\)
- Answer
-
1) \( \bigg(\dfrac{1}{2} \bigg)^{-5} = \dfrac{1}{(\frac{1}{2})^5} = \dfrac{1}{\frac{1}{32}} = 32 \)
2) \(2^{-4} = \dfrac{1}{2^4} = \dfrac{1}{16} \)
3) \( (-2)^{-4} = \dfrac{1}{(-2)^4} = \dfrac{1}{16} \)
4) \( -2^{-4} = - \dfrac{1}{2^{4}} = - \dfrac{1}{16} \)
5) \( (-2)^{-3} = \dfrac{1}{(-2)^3} = \dfrac{1}{-8} = - \dfrac{1}{8} \)
6) \( -2^{-3}= - (2^{-3}) = - \dfrac{1}{(2)^3} = - \dfrac{1}{8} \)
7) \( x^{-1} = \dfrac{1}{x} \)
8) \( x^{-2} = \dfrac{1}{x^2} \)
9) \( x^{-3} = \dfrac{1}{x^3} \)
10) \( x^{-2023} = \dfrac{1}{x^{2023}} \)
11) \(2023^0 = 1 \)
It is important that we understand the rules when it comes to working with exponents. These rules are summarized below.
Theorem: Let \(a\) and \(b\) be real numbers and \(m\) and \(n\) be integers. Then we have the following:
1) \( a^m a^n = a^{m+n} \)
2) \( \frac{a^m}{a^n} = a^{m-n} \)
3) \( \bigg( a^m \bigg)^n = a^{mn} \)
4) \( (ab)^n = a^n b^n \)
5) \( \displaystyle \bigg( \dfrac{a}{b} \bigg)^n = a^n b^n \)
Whenever a theorem is presented to you, a good idea is to take a few moments and translate the symbols into words. The above theorem is saying the following:
1) In order to multiply two powers with the same base, we add the exponents.
2) In order to divide two powers with the same base, we subtract the exponents.
3) Whenever we raise a power to a new power, we multiply the exponents.
4) To raise a product to a power, raise each factor to the power.
5) To raise a quotient to a power, raise both numerator and denominator to the power.
With these ideas in mind, allow us to try a few examples.
Perform the given operation using the multiplication properties of exponents and write your answer in simplest form:
- \(b^{2} \cdot b^{3}=b^{2+3}=b^{5}\)
- \(x^{8} x^{7}=x^{8+7}=x^{15}\)
- \(a^{8} a^{9} a^{14}=a^{8+9+14}=a^{31}\)
- \(4 x^{4} \cdot 7 x^{6}=(4 \cdot 7)\left(x^{4} \cdot x^{6}\right)=28 x^{10}\)
- \(5 x y^{3} \cdot 6 y=(5 \cdot 6)(x)\left(y^{3} \cdot y\right)=30 x y^{4}\)
- \(\left(5 x^{4} y^{2}\right)\left(2 x^{7} y^{3}\right)=10 x^{4+7} y^{2+3}=10 x^{11} y^{5}\)
- \((2 x)^{3}=2^{3} x^{3}=8 x^{3}\)
- \(\left(-4 a^{2} b^{5}\right)^{3}=(-4)^{3} a^{2 \cdot 3} b^{5 \cdot 3}=-64 a^{6} b^{15}\)
- \(\begin{align*}\left(-5 r^{3} s\right)^{2} \cdot\left(2 r^{4} s^{3}\right)^{3} \cdot\left(-r^{2} s^{2}\right) &=(-5)^{2} r^{3 \cdot 2} s^{2} \cdot 2^{3} r^{4 \cdot 3} s^{3 \cdot 3} \cdot(-1) r^{2} s^{2} \\&=25 r^{6} s^{2} \cdot 8 r^{12} s^{9} \cdot(-1) r^{2} s^{2} \\&=-200 r^{20} s^{13}\end{align*}\)
- \(\dfrac{x^{5}}{x^{3}}=\dfrac{x \cdot x \cdot x \cdot x \cdot x}{x \cdot x \cdot x}=\dfrac{x \cdot x}{1}=\dfrac{x^{2}}{1}=x^{2}\)
- \(\dfrac{x^{3}}{x^{5}}=\dfrac{x \cdot x \cdot x}{x \cdot x \cdot x \cdot x \cdot x}=\dfrac{1}{x \cdot x}=\dfrac{1}{x^{2}}\)
- \(\left(\dfrac{x}{y}\right)^{5}=\dfrac{x}{y} \cdot \dfrac{x}{y} \cdot \dfrac{x}{y} \cdot \dfrac{x}{y} \cdot \dfrac{x}{y}=\dfrac{x \cdot x \cdot x \cdot x \cdot x}{y \cdot y \cdot y \cdot y \cdot y}=\dfrac{x^{5}}{y^{5}}\)
Perform the given operation using the division properties of exponents and state your answer in simplest form:
- \(\dfrac{b^{8}}{b^{7}}=b^{8-7}=b^{1}=b\)
- \(\dfrac{x^{12} y^{2}}{x^{8} y}=x^{12-8} y^{2-1}=x^{4} y\)
- \(\dfrac{8 x^{6} y^{2}}{6 x^{5} y^{7}}=\dfrac{4 x^{6-5}}{3 y^{7-2}}=\dfrac{4 x^{1}}{3 y^{5}}=\dfrac{4 x}{3 y^{5}}\)
- \(\dfrac{\left(m^{2}\right)^{3}\left(n^{4}\right)^{5}}{\left(m^{3}\right)^{3}}=\dfrac{m^{6} n^{20}}{m^{9}}=\dfrac{n^{20}}{m^{3}}\)
- \(\left(\dfrac{3 a^{2} b^{4}}{9 c^{3}}\right)^{2}=\left(\dfrac{a^{2} b^{4}}{3 c^{3}}\right)^{2}=\dfrac{a^{2 \cdot 2} b^{4 \cdot 2}}{3^{2} c^{3 \cdot 2}}=\dfrac{a^{4} b^{8}}{9 c^{6}}\)Another way to simplify this correctly is this: \(\left(\dfrac{3 a^{2} b^{4}}{9 c^{3}}\right)^{2}=\dfrac{3^{2} a^{2 \cdot 2} b^{4 \cdot 2}}{9^{2} c^{3 \cdot 2}}=\dfrac{9 a^{4} b^{8}}{81 c^{6}}=\dfrac{a^{4} b^{8}}{9 c^{6}}\)
Perform the given operation and write your answer using positive exponents only
- \(\dfrac{x^{4} y^{2}}{x^{3} y^{-3}}=x^{4-3} y^{2-(-3)}=x y^{5}\)
- \(\left(x^{2} y\right) \cdot\left(x y^{-4}\right)=x^{2+1} y^{1+(-4)}=\dfrac{x^{3}}{y^{3}}\)
We will now turn our attention to the second question asked earlier. Namely, is it possible for \(n\) to not be an integer? For instance, what does \(5^{20.23} \) mean? In order to answer this, we must introduce the notion of a radical or root.
Definition: Let \(a\) denote a non-negative real number (meaning \(a\) is either positive or zero). The square root of \(a\), denoted by \( \sqrt{a} \) or \( \sqrt[2]{a} \) is said to equal \(b\) provided that \(b \geq 0\) and \(b^2 = a\). That is,
\[ \sqrt[2]{a} = b ~~ \text{means} ~~ b^2 = a ~~\text{and} ~~ b \geq 0\nonumber\ \]
Again, allow us to reflect on this definition. We may wonder, why does \(a\) have to be positive or zero? Notice that \(a = b^2 \) and for all real numbers \(b\), \(b^2 \geq 0 \). Hence \(a\) must also be greater than or equal to 0 and so \(a\) must either be positive or zero. Or quite simply, if \( b^2 = a \) and since and real number raised to the power of 2 is positive or zero, then \(a\) must be positive or zero. This will be important later on!
Additionally, we may wonder why is it that we require \(b \geq 0 \). The answer to this will be discussed on Day 2 since the explanation requires us to understand what is a function . Allow us to now consider an example.
\[ \sqrt{16} = 4 ~~ \text{because} ~~ 4^2 = 16 ~~\text{and} ~~ 4 \geq 0 \nonumber\ \]
Notice that
\[ \sqrt{16} \neq -4 \nonumber\ \]
Although it is true that \( (-4)^2 = 16 \), it is not true that \( -4 \geq 0\) and so \( \sqrt{16} \neq -4 \nonumber\ \). In summary, the square root symbol, \( \sqrt{~~} \) means "the positive square root of".
With regards to square roots, we will now pose an interesting question.
Suppose \(a\) is some real number. Is it always true that \( \sqrt{a^2} = a\)? Discuss.
- Answer
-
To answer questions like these, allow us to substitute in a few values for \(a\) in order to investigate the statement. If \(a\) is any real number, then \(a\) can be positive, negative or zero. Let us first choose a positive value for \(a\), say 3. Is it true that \( \sqrt{3^2} = 3\)? Yes!
Let us now choose a negative value for \(a\), say \( -3 \). Is it true that \( \sqrt{(-3)^2} = - 3\)? No!
And so the equation \( \sqrt{a^2} = a\) is not always true. In fact, the equation is only true when \(a \geq 0 \).
More generally, we should note the following:
\[ \text{For all real numbers} ~ a, \sqrt{a^2} = |a| \nonumber\ \]
However, there is nothing special about the square root. That is, we can extend this idea. If \[ \sqrt[2]{a} = b ~~ \text{means} ~~ b^2 = a ~~\text{and} ~~ b \geq 0\nonumber\ \] then it makes sense to say \[ \sqrt[4]{a} = b ~~ \text{means} ~~ b^4 = a \nonumber\ \] and \[ \sqrt[6]{a} = b ~~ \text{means} ~~ b^6 = a ~~\text{and} ~~ b \geq 0\nonumber\ \] and so on. More generally, we present the following definition:
Definition: Let \(a\) denote a non-negative real number (meaning \(a\) is either positive or zero) and let \(n\) denote any positive even integer. Then the \(n^{th} \) root of \(a\) is defined as follows:
\[ \sqrt[n]{a} = b ~~ \text{means} ~~ b^n = a ~~\text{and} ~~ b \geq 0\nonumber\ \]
The above definition is saying if \(n\) is even, then to find \( \sqrt[n]{a} \), we require both \(a\) and \(b\) to be positive.
Evaluate the following:
1) \( \sqrt{25} \)
2) \( \sqrt[4]{81} \)
3) \( \sqrt[6]{64} \)
4) \( \sqrt[6]{-64} \)
- Answer
-
1) To find \( \sqrt{25} \) we must ask ourselves can we find a real number \(b\) such that \(b^2 = 25 \) and \(b \geq 0\)? The answer is yes - if we take \(b = 5 \) then \(b^2 = 25 \) and \(b \geq 0\).
2) To find \( \sqrt[4]{81} \) we must ask ourselves can we find a real number \(b\) such that \(b^4 = 81 \) and \(b \geq 0\)? The answer is yes - if we take \(b = 3 \) then \(b^4 = 81 \) and \(b \geq 0\).
3) To find \( \sqrt[6]{64} \) we must ask ourselves can we find a real number \(b\) such that \(b^6 = 64 \) and \(b \geq 0\)? The answer is yes - if we take \(b = 2 \) then \(b^6 = 64 \) and \(b \geq 0\).
4) \( \sqrt[6]{-64} \) we must ask ourselves can we find a real number \(b\) such that \(b^6 = -64 \) and \(b \geq 0\)? The answer here is no. Notice for any real number \(b\), \(b^6 \) will be positive or zero and so \(b^6 \) can never be equal to \( - 64 \). Hence the answer is that \( \sqrt[6]{-64} \) is not defined. Similarly, \( \sqrt[2]{-64} \) and \( \sqrt[4]{-64} \) are not defined.
Notice that the last part of the above example suggests that for even roots, the number inside the root cannot be negative. Allow us to now discuss odd roots.
Definition: Let \(a\) denote a real number (meaning \(a\) is either positive, negative or zero) and let \(n\) denote any positive odd integer. Then the \(n^{th} \) root of \(a\) is defined as follows:
\[ \sqrt[n]{a} = b ~~ \text{means} ~~ b^n = a \nonumber\ \]
Notice in the above definition for odd roots, we now allow the number inside the root to be negative and we dropped the condition that \(b \geq 0 \).
Evaluate the following:
1) \( \sqrt[3]{8} \)
2) \( \sqrt[3]{-8} \)
3) \( \sqrt[3]{10^3} \)
4) \( \sqrt[3]{(-10)^3} \)
- Answer
-
1) To find\( \sqrt[3]{8} \) we must ask ourselves can we find a real number \(b\) such that \(b^3 = 8 \)? The answer is yes - if we take \(b = 2 \) then \(b^3 = 8 \).
2) To find \( \sqrt[3]{-8} \) we must ask ourselves can we find a real number \(b\) such that \(b^3 = -8 \)? The answer is yes - if we take \(b = -2 \) then \(b^3 = -8 \).
-
3) To find \( \sqrt[3]{10^3} \) we must ask ourselves can we find a real number \(b\) such that \(b^3 = 10^3 \)? The answer is yes - if we take \(b = 10 \) then \(b^3 = 10^3 \).
4) To find \( \sqrt[3]{(-10)^3} \) we must ask ourselves can we find a real number \(b\) such that \(b^3 = (-10)^3 \)? The answer is yes - if we take \(b =- 10 \) then \(b^3= (-10)^3 \).
The above examples can be briefly summarized as the following:
1) \( \sqrt[n]{a^n} = a \nonumber\ \) if \(n\) is a positive odd integer.
2) \( \sqrt[n]{a^n} = |a| \nonumber\ \) if \(n\) is a positive even integer.
2) We cannot take the \(n^{th}\) root of a negative number when \(n\) is a positive even integer. However, we can take the \(n^{th}\) root of a negative number when \(n\) is a positive odd integer.
When it comes to \(n^{th} \) roots, we should be familiar with their properties:
Theorem:
1) \( \sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b} \)
2) \( \sqrt[n]{\dfrac{a}{b}} = \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}} \)
3) \( \sqrt[m]{\sqrt[n]{a}} = \sqrt[mn]{a} \)
Take a moment and try to translate the above theorem into words.
- Answer
-
1) The \(n^{th} \) root of a product is the product of the individual \(n^{th} \) roots.
2) The \(n^{th} \) root of a quotient is the quotient of the individual \(n^{th} \) roots.
3) The \(m^{th} \) root of the \(n^{th} \) root is the same as the \(mn^{th} \) root.
Simplifythe following expressions as much as possible:
1) \( \sqrt[3]{x^4} \)
2) \( \sqrt[4]{81x^8 y^4 } \)
- Answer
-
1) \begin{align*} \sqrt[3]{x^4} &= \sqrt[3]{x^3 x } \\ &= \sqrt[3]{x^3 } \sqrt[3]{x } \\ &= x \sqrt[3]{x } \end{align*}
2) \begin{align*} \sqrt[4]{81x^8 y^4 } &= \sqrt[4]{81 } \sqrt[4]{x^8 } \sqrt[4]{y^4 } \\ &= 3 \sqrt[4]{ (x^2)^4 } |y| \\ &= 3 |x^2| |y| \\ &= 3x^2 |y| \end{align*}
We now make one final extension via the following definition.
Definition: For any rational exponent \( \frac{m}{n} \) in lowest terms and \(n > 0 \), we define
\[ a^{\dfrac{m}{n}} = (\sqrt[n]{a})^m \nonumber\ \] or equivalently \[ a^{\dfrac{m}{n}} = (\sqrt[n]{a^m}) \nonumber\ \]
If \(n\) is even, then we require \(a \geq 0\).
Express the following roots in terms of a rational exponent.
1) \( \sqrt{x} \)
2) \( \sqrt[3]{x} \)
3) \( \sqrt[3]{x^4} \)
4) \( 8^{\frac{2}{3}} \)
5) \( 125^{-\frac{1}{3}} \)
- Answer
-
1) \( \sqrt{x} = x^{\frac{1}{2}} \)
2) \( \sqrt[3]{x} = x^{\frac{1}{3}} \)
3) \( \sqrt[3]{x^4} = x^{\frac{4}{3}} \)
4) \( 8^{\frac{2}{3}} = \sqrt[3]{8^2} = \sqrt[3]{64} = 4 \) or \( 8^{\frac{2}{3}} = (\sqrt[3]{8})^2 = 2^2 = 4 \)
5) \( 125^{-\frac{1}{3}} = \frac{1}{125^{\frac{1}{3}}} = \frac{1}{\sqrt[3]{125}} = \frac{1}{5} \)
Note that The Law of Exponents also applies to when the powers are rational numbers and not just integers.
Theorem: Let \(a\) and \(b\) be real numbers and \(m\) and \(n\) be rational numbers. Then we have the following:
1) \( a^m a^n = a^{m+n} \)
2) \( \frac{a^m}{a^n} = a^{m-n} \)
3) \( \bigg( a^m \bigg)^n = a^{mn} \)
4) \( (ab)^n = a^n b^n \)
5) \( \displaystyle \bigg( \dfrac{a}{b} \bigg)^n = a^n b^n \)
Allow us to now work through a few examples.
Simplify the following:
1) \( x^{\frac{1}{3}} x^{\frac{7}{3}} \)
2) \( \frac{10x^{\frac{5}{6}} }{2x^{\frac{7}{6}}} \)
3) \( ( 4a^5 b^7)^{\frac{1}{2}} \)
- Answer
-
1) \[ x^{\frac{1}{3}} x^{\frac{7}{3}} = x^{ \frac{1}{3} + \frac{7}{3} } = x^{ \frac{8}{3}} \nonumber \]
2) \[\frac{10x^{\frac{5}{6}} }{2x^{\frac{7}{6}}} = \frac{10}{2} \frac{x^{\frac{5}{6}}}{x^{\frac{7}{6}}} = 5 x^{\frac{5}{6} - \frac{7}{6} } = 5x^{- \frac{2}{6}} = 5x^{- \frac{1}{3}} \nonumber \]
3) \[ ( 4a^5 b^7)^{\frac{1}{2}} = 4^{\frac{1}{2}} (a^5)^{\frac{1}{2}} (b^7)^{\frac{1}{2}} = 2 a^{\frac{5}{2}} b^{\frac{7}{2}} \nonumber \]


12.12.1: Ethics
selected template will load here
This action is not available.
The term ethics is defined as “a set of moral principles” or “the principles of conduct governing an individual or a group.” [1] Since the dawn of civilization, the study of ethics and their impact has fascinated mankind. But what do ethics have to do with information systems?
The introduction of new technology can have a profound effect on human behavior. New technologies give us capabilities that we did not have before, which in turn create environments and situations that have not been specifically addressed in ethical terms. Those who master new technologies gain new power; those who cannot or do not master them may lose power. In 1913, Henry Ford implemented the first moving assembly line to create his Model T cars. While this was a great step forward technologically (and economically), the assembly line reduced the value of human beings in the production process. The development of the atomic bomb concentrated unimaginable power in the hands of one government, who then had to wrestle with the decision to use it. Today’s digital technologies have created new categories of ethical dilemmas.
For example, the ability to anonymously make perfect copies of digital music has tempted many music fans to download copyrighted music for their own use without making payment to the music’s owner. Many of those who would never have walked into a music store and stolen a CD find themselves with dozens of illegally downloaded albums.
Digital technologies have given us the ability to aggregate information from multiple sources to create profiles of people. What would have taken weeks of work in the past can now be done in seconds, allowing private organizations and governments to know more about individuals than at any time in history. This information has value, but also chips away at the privacy of consumers and citizens.