Simplify ((9xy)^2)/((3x)^3)

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

Step 1

Simplify the numerator.

Apply the product rule to $9 x y$ .

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

Apply the product rule to $9 x$ .

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

Raise $9$ to the power of $2$ .

$\frac{81 x^{2} y^{2}}{{(3 x)}^{3}}$

$\frac{81 x^{2} y^{2}}{{(3 x)}^{3}}$

Step 2

Simplify the denominator.

Apply the product rule to $3 x$ .

$\frac{81 x^{2} y^{2}}{3^{3} x^{3}}$

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

$\frac{81 x^{2} y^{2}}{27 x^{3}}$

$\frac{81 x^{2} y^{2}}{27 x^{3}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $81$ and $27$ .

Factor $27$ out of $81 x^{2} y^{2}$ .

$\frac{27 (3 x^{2} y^{2})}{27 x^{3}}$

Cancel the common factors.

Factor $27$ out of $27 x^{3}$ .

$\frac{27 (3 x^{2} y^{2})}{27 (x^{3})}$

Cancel the common factor.

$\frac{27 (3 x^{2} y^{2})}{27 x^{3}}$

Rewrite the expression.

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

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

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

Cancel the common factor of $x^{2}$ and $x^{3}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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