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

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

Step 1

Cancel the common factor of $x$ and $x^{3}$ .

Factor $x$ out of $3 x y^{2}$ .

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

Cancel the common factors.

Factor $x$ out of $x^{3} y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

Factor $y$ out of $3 y^{2}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

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

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

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

Apply the product rule to $3 y$ .

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

Step 5

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

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

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

Multiply $2$ by $2$ .

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

Step 6

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

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