Simplify (-4^-2y)^2

${(- 4^{- 2} y)}^{2}$

Step 1

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

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

Step 2

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

${(- \frac{1}{16} y)}^{2}$

Step 3

Combine $y$ and $\frac{1}{16}$ .

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

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{y}{16}$ .

${(- 1)}^{2} {(\frac{y}{16})}^{2}$

Apply the product rule to $\frac{y}{16}$ .

${(- 1)}^{2} \frac{y^{2}}{16^{2}}$

Step 5

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

$1 \frac{y^{2}}{16^{2}}$

Step 6

Multiply $\frac{y^{2}}{16^{2}}$ by $1$ .

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

Step 7

Raise $16$ to the power of $2$ .

$\frac{y^{2}}{256}$