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

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

Step 1

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

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

Multiply $2$ by $2$ .

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

Step 6

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

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

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

Multiply $2$ by $2$ .

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