Simplify 8/(4^-2)

$\frac{8}{4^{- 2}}$

Move $4^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$8 \cdot 4^{2}$

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

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

Rewrite $4$ as $2^{2}$ .

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

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

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

$2^{3} \cdot 2^{2 \cdot 2}$

Multiply $2$ by $2$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{3 + 4}$

Add $3$ and $4$ .

$2^{7}$

Raise $2$ to the power of $7$ .

$128$