In a test I'll take there may be a question such as the following:
A perfect power is an integer that can be written as $a^b$, $a$ and $b$ being integers greater or equal to 2.
One of the following numbers is not a perfect power, which one is it?
The first three (125, 216, 1000) are simply
primeNumber^something, but the last two aren't.
Keeping in mind that I can't use a calculator and should spend on average only 1 minute per question, I was wondering what's the best method I can use to resolve such questions or more difficult ones (where there are less obvious wrong solutions, such as 1000).