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

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

Step 1

Simplify the expression.

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

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

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Multiply $- - \frac{1}{3}$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{1}{3}$ by $1$ .

$64^{\frac{1}{3}}$

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 2

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$4^{1}$

Step 3

Evaluate the exponent.

$4$