Question

What is the value of the power a if 5 to the power of a is equal to 1/125

Answer 1

First of all, you should know/notice that

$125=5^3$

You should also know how negative exponents work:

$a^{-m}=\dfrac{1}{a^m}$

So, if you wanted

$5^x=125$

the answer would be x=3, but since you want 125 to be at the denominator, the answer is x=-3:

$5^{-3}=\dfrac{1}{5^3}=\dfrac{1}{125}$