section_path: Terminology
section_name: Terminology
paragraph_text: Terminology
  
  The expression b = b · b is called "the square of b " or " b squared", because the area of a square with side-length b is b. (It is true that it could also be called " b to the second power", but "the square of b " and " b squared" are so ingrained by tradition and convenience that " b to the second power" tends to sound unusual or clumsy.)
  
  Similarly, the expression b = b · b · b is called "the cube of b " or " b cubed", because the volume of a cube with side-length b is b.
  
  When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power.
  
  The word "raised" is usually omitted, and sometimes "power" as well, so 3 can be simply read "3 to the 5th", or "3 to the 5". Therefore, the exponentiation b can be expressed as " b to the power of n ", " b to the n th power", " b to the n th", or most briefly as " b to the n ".