Evaluate (45x^4y^6)/((5xy)^3)

$\frac{45 x^{4} y^{6}}{{(5 x y)}^{3}}$

Simplify the denominator.

Apply the product rule to $5 x y$ .

$\frac{45 x^{4} y^{6}}{{(5 x)}^{3} y^{3}}$

Apply the product rule to $5 x$ .

$\frac{45 x^{4} y^{6}}{5^{3} x^{3} y^{3}}$

Raise $5$ to the power of $3$ .

$\frac{45 x^{4} y^{6}}{125 x^{3} y^{3}}$

$\frac{45 x^{4} y^{6}}{125 x^{3} y^{3}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $45$ and $125$ .

Factor $5$ out of $45 x^{4} y^{6}$ .

$\frac{5 (9 x^{4} y^{6})}{125 x^{3} y^{3}}$

Cancel the common factors.

Factor $5$ out of $125 x^{3} y^{3}$ .

$\frac{5 (9 x^{4} y^{6})}{5 (25 x^{3} y^{3})}$

Cancel the common factor.

$\frac{5 (9 x^{4} y^{6})}{5 (25 x^{3} y^{3})}$

Rewrite the expression.

$\frac{9 x^{4} y^{6}}{25 x^{3} y^{3}}$

$\frac{9 x^{4} y^{6}}{25 x^{3} y^{3}}$

$\frac{9 x^{4} y^{6}}{25 x^{3} y^{3}}$

Cancel the common factor of $x^{4}$ and $x^{3}$ .

Factor $x^{3}$ out of $9 x^{4} y^{6}$ .

$\frac{x^{3} (9 x y^{6})}{25 x^{3} y^{3}}$

Cancel the common factors.

Factor $x^{3}$ out of $25 x^{3} y^{3}$ .

$\frac{x^{3} (9 x y^{6})}{x^{3} (25 y^{3})}$

Cancel the common factor.

$\frac{x^{3} (9 x y^{6})}{x^{3} (25 y^{3})}$

Rewrite the expression.

$\frac{9 x y^{6}}{25 y^{3}}$

$\frac{9 x y^{6}}{25 y^{3}}$

$\frac{9 x y^{6}}{25 y^{3}}$

Cancel the common factor of $y^{6}$ and $y^{3}$ .

Factor $y^{3}$ out of $9 x y^{6}$ .

$\frac{y^{3} (9 x y^{3})}{25 y^{3}}$

Cancel the common factors.

Factor $y^{3}$ out of $25 y^{3}$ .

$\frac{y^{3} (9 x y^{3})}{y^{3} \cdot 25}$

Cancel the common factor.

$\frac{y^{3} (9 x y^{3})}{y^{3} \cdot 25}$

Rewrite the expression.

$\frac{9 x y^{3}}{25}$

$\frac{9 x y^{3}}{25}$

$\frac{9 x y^{3}}{25}$

$\frac{9 x y^{3}}{25}$

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