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)=(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)=(1)/(5^3)=(1)/(125)`