Simplify ((1/2)^-4)^2

${({(\frac{1}{2})}^{- 4})}^{2}$

Multiply the exponents in ${({(\frac{1}{2})}^{- 4})}^{2}$ .

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

${(\frac{1}{2})}^{- 4 \cdot 2}$

Multiply $- 4$ by $2$ .

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

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

$2^{8}$

Raise $2$ to the power of $8$ .

$256$