Evaluate (1/125)^(-2/3)

${(\frac{1}{125})}^{- \frac{2}{3}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

$125^{\frac{2}{3}}$

Step 2

Simplify the expression.

Rewrite $125$ as $5^{3}$ .

${(5^{3})}^{\frac{2}{3}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$5^{3 (\frac{2}{3})}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$5^{3 (\frac{2}{3})}$

Rewrite the expression.

$5^{2}$

Step 4

Raise $5$ to the power of $2$ .

$25$