Evaluate ((1/8)^(1/3))^-2

${({(\frac{1}{8})}^{\frac{1}{3}})}^{- 2}$

Step 1

Multiply the exponents in ${({(\frac{1}{8})}^{\frac{1}{3}})}^{- 2}$ .

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

${(\frac{1}{8})}^{\frac{1}{3} \cdot - 2}$

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

${(\frac{1}{8})}^{\frac{- 2}{3}}$

Move the negative in front of the fraction.

${(\frac{1}{8})}^{- \frac{2}{3}}$

Step 2

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

$8^{\frac{2}{3}}$

Step 3

Simplify the expression.

Rewrite $8$ as $2^{3}$ .

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

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

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{2}$

Step 5

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

$4$