Simplify (-1/64)^(-1/3)

${(- \frac{1}{64})}^{- \frac{1}{3}}$

Step 1

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

${(- 64)}^{\frac{1}{3}}$

Step 2

Simplify the expression.

Rewrite $- 64$ as ${(- 4)}^{3}$ .

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

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

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

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

${(- 4)}^{1}$

Step 4

Evaluate the exponent.

$- 4$