Question

What is the value of the base in the power (-125)-3?

Answer 1

A power is something like \[a^b\]where a is the base and b is the exponent.
The power\[(-125)^{-3}\]would have base -125 then.
It could be, however, that you are supposed to simplify this power a bit before answering the question. It is easy to see that \[(-125)^{-3}= -(125)^{-3}\]So you could say the base is 125.
Also, you could rewrite the power to get a positive exponent, using the rule:\[a^{-b}=\frac{ 1 }{ a^b }\]Your power would then be:\[-\frac{ 1 }{ 125^3 }=-\frac{ 1^3 }{ 125^3 } =-\left( \frac{ 1 }{ 125 } \right)^3\]so the base is 1/125.
As soon as you realize that 125 = 5³, you can go even further with this "base game"...