Simplify (36x^4y^5)/((3xy)^2)

$\frac{36 x^{4} y^{5}}{{(3 x y)}^{2}}$

Step 1

Simplify the denominator.

Apply the product rule to $3 x y$ .

$\frac{36 x^{4} y^{5}}{{(3 x)}^{2} y^{2}}$

Apply the product rule to $3 x$ .

$\frac{36 x^{4} y^{5}}{3^{2} x^{2} y^{2}}$

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

$\frac{36 x^{4} y^{5}}{9 x^{2} y^{2}}$

$\frac{36 x^{4} y^{5}}{9 x^{2} y^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $36$ and $9$ .

Factor $9$ out of $36 x^{4} y^{5}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cancel the common factor of $x^{4}$ and $x^{2}$ .

Factor $x^{2}$ out of $4 x^{4} y^{5}$ .

$\frac{x^{2} (4 x^{2} y^{5})}{x^{2} y^{2}}$

Cancel the common factors.

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

$\frac{x^{2} (4 x^{2} y^{5})}{x^{2} (y^{2})}$

Cancel the common factor.

$\frac{x^{2} (4 x^{2} y^{5})}{x^{2} y^{2}}$

Rewrite the expression.

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

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

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

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

Factor $y^{2}$ out of $4 x^{2} y^{5}$ .

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

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{2} (4 x^{2} y^{3})}{y^{2} \cdot 1}$

Cancel the common factor.

$\frac{y^{2} (4 x^{2} y^{3})}{y^{2} \cdot 1}$

Rewrite the expression.

$\frac{4 x^{2} y^{3}}{1}$

Divide $4 x^{2} y^{3}$ by $1$ .

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

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

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

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

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