Simplify ((2^-1)/(2^0))^-2

${(\frac{2^{- 1}}{2^{0}})}^{- 2}$

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

${(\frac{1}{2^{0} \cdot 2})}^{- 2}$

Simplify the denominator.

Multiply $2^{0}$ by $2$ by adding the exponents.

Multiply $2^{0}$ by $2$ .

Raise $2$ to the power of $1$ .

${(\frac{1}{2^{0} \cdot 2^{1}})}^{- 2}$

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

${(\frac{1}{2^{0 + 1}})}^{- 2}$

Add $0$ and $1$ .

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

Simplify $2^{1}$ .

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

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

$2^{2}$

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

$4$