Simplify ((x/2)^-2)/((y/4)^-2)

$\frac{{(\frac{x}{2})}^{- 2}}{{(\frac{y}{4})}^{- 2}}$

Simplify the expression.

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

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

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

$\frac{{(\frac{y}{4})}^{2}}{{(\frac{x}{2})}^{2}}$

Simplify the numerator.

Apply the product rule to $\frac{y}{4}$ .

$\frac{\frac{y^{2}}{4^{2}}}{{(\frac{x}{2})}^{2}}$

Raise $4$ to the power of $2$ .

$\frac{\frac{y^{2}}{16}}{{(\frac{x}{2})}^{2}}$

Simplify the denominator.

Apply the product rule to $\frac{x}{2}$ .

$\frac{\frac{y^{2}}{16}}{\frac{x^{2}}{2^{2}}}$

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

$\frac{\frac{y^{2}}{16}}{\frac{x^{2}}{4}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{y^{2}}{16} \cdot \frac{4}{x^{2}}$

Combine.

$\frac{y^{2} \cdot 4}{16 x^{2}}$

Cancel the common factor of $4$ and $16$ .

Factor $4$ out of $y^{2} \cdot 4$ .

$\frac{4 \cdot y^{2}}{16 x^{2}}$

Cancel the common factors.

Factor $4$ out of $16 x^{2}$ .

$\frac{4 \cdot y^{2}}{4 (4 x^{2})}$

Cancel the common factor.

$\frac{4 \cdot y^{2}}{4 (4 x^{2})}$

Rewrite the expression.

$\frac{y^{2}}{4 x^{2}}$