31
^{32}
?
27
^{32}

>

=

<

When we want to compare two powers with the same base we just have to compare the exponents and which has the higher exponent is the larger number.

When we want to compare two powers with the same exponents we just have to compare the bases and which has the higher base is the larger number.

In order to compare two powers with different bases or exponents we have to bring the bases to the same base or to bring the exponents to the same exponent and then the numbers can be compared.

By learning math, you learn to think.