Simplify ((1/64)^(1/3))^-2

${({(\frac{1}{64})}^{\frac{1}{3}})}^{- 2}$

Multiply the exponents in ${({(\frac{1}{64})}^{\frac{1}{3}})}^{- 2}$ .

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

${(\frac{1}{64})}^{\frac{1}{3} \cdot - 2}$

Combine $\frac{1}{3}$ and $- 2$ .

${(\frac{1}{64})}^{\frac{- 2}{3}}$

Move the negative in front of the fraction.

${(\frac{1}{64})}^{- \frac{2}{3}}$

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

$64^{\frac{2}{3}}$

Simplify the expression.

Rewrite $64$ as $4^{3}$ .

${(4^{3})}^{\frac{2}{3}}$

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

$4^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$4^{3 (\frac{2}{3})}$

Rewrite the expression.

$4^{2}$

Raise $4$ to the power of $2$ .

$16$