Final answer:
In mathematics, a perfect power is an integer that can be written as one integer raised to the power of another. The perfect powers from the given options are 1 (a), 27 (c), and 100 (e).
Step-by-step explanation:
In mathematics, a perfect power is a positive integer that can be expressed as an integer power of another positive integer, meaning it can be written as x^n where x is a positive integer and n is an integer greater than 1. Let's evaluate the given options to determine which are perfect powers:
- 1: This is a perfect power because 1 = 12, 13, ..., 1 to any power.
- 24: This number is not a perfect power as it cannot be written as an integer to an integer power greater than 1 without involving fractions or decimals.
- 27: This is a perfect power because 27 = 33.
- 81: This is also a perfect power because 81 = 34.
- 99: This number is not a perfect power for the same reason as 24.
- 100: This is a perfect power because 100 = 102.
The final answer identifying the perfect powers from the options given is: a, c, and e.