Simplify ((1/64)^(1/3))^-4

${({(\frac{1}{64})}^{\frac{1}{3}})}^{- 4}$

Step 1

Multiply the exponents in ${({(\frac{1}{64})}^{\frac{1}{3}})}^{- 4}$ .

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

${(\frac{1}{64})}^{\frac{1}{3} \cdot - 4}$

Combine $\frac{1}{3}$ and $- 4$ .

${(\frac{1}{64})}^{\frac{- 4}{3}}$

Move the negative in front of the fraction.

${(\frac{1}{64})}^{- \frac{4}{3}}$

Step 2

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

$64^{\frac{4}{3}}$

Step 3

Simplify the expression.

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

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

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

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$4^{4}$

Step 5

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

$256$