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Evaluate -(1/125)^(-4/3)

$- {(\frac{1}{125})}^{- \frac{4}{3}}$

Step 1

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

$- 125^{\frac{4}{3}}$

Step 2

Simplify the expression.

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

$- {(5^{3})}^{\frac{4}{3}}$

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

$- 5^{3 (\frac{4}{3})}$

$- 5^{3 (\frac{4}{3})}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$- 5^{3 (\frac{4}{3})}$

Rewrite the expression.

$- 5^{4}$

$- 5^{4}$

Step 4

Simplify the expression.

Raise $5$ to the power of $4$ .

$- 1 \cdot 625$

Multiply $- 1$ by $625$ .

$- 625$

$- 625$

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