Simplify ((3xy)/(2x^2))^-2

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

Step 1

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $3 x y$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

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

Apply the product rule to $2 x$ .

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

Apply the product rule to $3 y$ .

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

Step 4

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

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

Step 5

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

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