Simplify ((2x)/(3y^-1))^2

${(\frac{2 x}{3 y^{- 1}})}^{2}$

Step 1

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

${(\frac{2 x y}{3})}^{2}$

Step 2

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

Apply the product rule to $\frac{2 x y}{3}$ .

$\frac{{(2 x y)}^{2}}{3^{2}}$

Apply the product rule to $2 x y$ .

$\frac{{(2 x)}^{2} y^{2}}{3^{2}}$

Apply the product rule to $2 x$ .

$\frac{2^{2} x^{2} y^{2}}{3^{2}}$

Step 3

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

$\frac{4 x^{2} y^{2}}{3^{2}}$

Step 4

Raise $3$ to the power of $2$ .

$\frac{4 x^{2} y^{2}}{9}$