Simplify (45x^11y^3)/((3x)^2*xy)

$\frac{45 x^{11} y^{3}}{{(3 x)}^{2} \cdot x y}$

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{11}$ and $x$ .

Factor $x$ out of $45 x^{11} y^{3}$ .

$\frac{x (45 x^{10} y^{3})}{{(3 x)}^{2} \cdot (x y)}$

Cancel the common factors.

Factor $x$ out of ${(3 x)}^{2} \cdot (x y)$ .

$\frac{x (45 x^{10} y^{3})}{x ({(3 x)}^{2} \cdot (y))}$

Cancel the common factor.

$\frac{x (45 x^{10} y^{3})}{x ({(3 x)}^{2} \cdot (y))}$

Rewrite the expression.

$\frac{45 x^{10} y^{3}}{{(3 x)}^{2} \cdot (y)}$

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

Factor $y$ out of $45 x^{10} y^{3}$ .

$\frac{y (45 x^{10} y^{2})}{{(3 x)}^{2} \cdot (y)}$

Cancel the common factors.

Factor $y$ out of ${(3 x)}^{2} \cdot (y)$ .

$\frac{y (45 x^{10} y^{2})}{y \cdot {(3 x)}^{2}}$

Cancel the common factor.

$\frac{y (45 x^{10} y^{2})}{y \cdot {(3 x)}^{2}}$

Rewrite the expression.

$\frac{45 x^{10} y^{2}}{{(3 x)}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $3 x$ .

$\frac{45 x^{10} y^{2}}{3^{2} x^{2}}$

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

$\frac{45 x^{10} y^{2}}{9 x^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $45$ and $9$ .

Factor $9$ out of $45 x^{10} y^{2}$ .

$\frac{9 (5 x^{10} y^{2})}{9 x^{2}}$

Cancel the common factors.

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

$\frac{9 (5 x^{10} y^{2})}{9 (x^{2})}$

Cancel the common factor.

$\frac{9 (5 x^{10} y^{2})}{9 x^{2}}$

Rewrite the expression.

$\frac{5 x^{10} y^{2}}{x^{2}}$

Cancel the common factor of $x^{10}$ and $x^{2}$ .

Factor $x^{2}$ out of $5 x^{10} y^{2}$ .

$\frac{x^{2} (5 x^{8} y^{2})}{x^{2}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{x^{2} (5 x^{8} y^{2})}{x^{2} \cdot 1}$

Cancel the common factor.

$\frac{x^{2} (5 x^{8} y^{2})}{x^{2} \cdot 1}$

Rewrite the expression.

$\frac{5 x^{8} y^{2}}{1}$

Divide $5 x^{8} y^{2}$ by $1$ .

$5 x^{8} y^{2}$

Simplify (45x^11y^3)/((3x)^2*xy)

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