why is (-125)^-2/3 1/25. why isn't it -1/25?

Answer 1

recall that a^(-x) = 1/a^x

having a negative exponent does not imply you get a negative answer.

so (-125)^-2/3 = 1/(-125)^(2/3)

= 1/[(-125)^(1/3)]^2

= 1/(-5)^2
= 1/25