Simplify (2^2)/((2^-4)^3)

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

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

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

Simplify the denominator.

Multiply the exponents in ${(2^{- 4})}^{3}$ .

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

$\frac{4}{2^{- 4 \cdot 3}}$

Multiply $- 4$ by $3$ .

$\frac{4}{2^{- 12}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4}{\frac{1}{2^{12}}}$

Raise $2$ to the power of $12$ .

$\frac{4}{\frac{1}{4096}}$

Multiply the numerator by the reciprocal of the denominator.

$4 \cdot 4096$

Multiply $4$ by $4096$ .

$16384$