Answer
$\dfrac{1}{25}$
Work Step by Step
We want to break down this problem a little to be able to work with it. The number $125$ can be broken down to a small base raised to a power: $5^3$. Let's rewrite the problem:
$(5^3)^{-2/3}$
Raising a power to a power means we can multiply the two powers or exponents together:
$5^{3(-2/3)}$
Multiply the exponents to simplify:
$5^{-6/3}$
Reduce the fraction in the exponent by dividing both numerator and denominator by the greatest common factor, which is $3$, in this case:
$5^{-2}$
Use the rule $a^{-m}=\dfrac{1}{a^m}$ to obtain:
$\dfrac{1}{5^{2}}$
Let's evaluate $5^2$:
$\dfrac{1}{25}$