Plans include only allowing children to start primary school once they have reached the age of four and moving to monthly bin collections.
Outsourcing waste collection, franchising school catering services and halving funding for Powys theatres are also being considered.
Council leader Barry Thomas said "very difficult choices" had to be made.
Other proposals include:
The cuts are in addition to reductions of nearly £40m the authority has made since 2012.
Mr Thomas said: "The cabinet's proposals will now be taken forward to a budget seminar for all members of council on 16th September, and later in September, the public will be consulted by an online budget simulator.
"This is a process where the public can indicate their priorities for achieving the required saving of £27m, and the outcome of this process will provide vital information for the cabinet and council to consider as the budget process moves forward."
Powys council's leaders are proposing major cuts to services as they seek to save £27m over the next three years.