Simplify (4x^-1y^2)^2

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

Step 1

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

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

Step 2

Combine $4$ and $\frac{1}{x}$ .

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

Step 3

Combine $\frac{4}{x}$ and $y^{2}$ .

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

Step 4

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

Apply the product rule to $\frac{4 y^{2}}{x}$ .

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

Apply the product rule to $4 y^{2}$ .

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

Step 5

Simplify the numerator.

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

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

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

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

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

Multiply $2$ by $2$ .

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