Simplify ((xy)^-2)/((3y)^2x^-5)

$\frac{{(x y)}^{- 2}}{{(3 y)}^{2} x^{- 5}}$

Step 1

Simplify the expression.

Move ${(x y)}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(3 y)}^{2} x^{- 5} {(x y)}^{2}}$

Move $x^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x^{5}}{{(3 y)}^{2} {(x y)}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $3 y$ .

$\frac{x^{5}}{3^{2} y^{2} {(x y)}^{2}}$

Apply the product rule to $x y$ .

$\frac{x^{5}}{3^{2} y^{2} x^{2} y^{2}}$

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{x^{5}}{3^{2} (y^{2} y^{2}) x^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{5}}{3^{2} y^{2 + 2} x^{2}}$

Add $2$ and $2$ .

$\frac{x^{5}}{3^{2} y^{4} x^{2}}$

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

$\frac{x^{5}}{9 y^{4} x^{2}}$

Step 3

Cancel the common factor of $x^{5}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{5}$ .

$\frac{x^{2} x^{3}}{9 y^{4} x^{2}}$

Cancel the common factors.

Factor $x^{2}$ out of $9 y^{4} x^{2}$ .

$\frac{x^{2} x^{3}}{x^{2} (9 y^{4})}$

Cancel the common factor.

$\frac{x^{2} x^{3}}{x^{2} (9 y^{4})}$

Rewrite the expression.

$\frac{x^{3}}{9 y^{4}}$