Stumped by a pretty basic fraction division

Question

I'm self-studying through Stroud & Booths's amazing "Engineering Mathematics", 7th Edition, and am still on the "Arithmetic" section. Even though I've gone through the whole chapter and a lot of the practice exercises, I'm still stumped by some occasionally. Here's one:

I'm supposed to present this fraction as a number raised to a power:

$$6^2 \div 5^{-2}$$

My trusty calculator says that the final result is 75, but that's not the point of the exercise. Any guidance, please? :)

Answer 1

First of all doesn't the calculation evaluate to 900? But if you want to put the final answer as a number to an exponent, here's what you do.

$6^2 / 5^{-2} = 6^2 / (1/5^2) = 6^2 * 5^2 = (6*5)^2 = 30^2$

Answer 2

$$ \frac{6^2}{5^{-2}} = 6^2\cdot 5^2 = 30^2=900. $$

Answer 3

Hint: Any number of the form $a^{-b}$ is the same as $1/a^b$.

For example, $a/c^{-b} = a/(1/c^b) = a*c^b$