Algebra Examples

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

Step 1

Cancel the common factor of $x^{4}$ and $x^{5}$ .

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Step 1.1

Factor $x^{4}$ out of ${(3 x y)}^{2} x^{4} y$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

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

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $3 x y$ .

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

Step 2.2

Combine exponents.

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Step 2.2.1

Raise $y$ to the power of $1$ .

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

Step 2.2.2

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

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

Step 2.2.3

Add $1$ and $2$ .

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

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

Step 2.3

Apply the product rule to $3 x$ .

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

Step 2.4

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

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

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

Step 3

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

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Step 3.1

Factor $x$ out of $9 x^{2} y^{3}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Raise $x$ to the power of $1$ .

$\frac{x (9 x y^{3})}{x^{1}}$

Step 3.2.2

Factor $x$ out of $x^{1}$ .

$\frac{x (9 x y^{3})}{x \cdot 1}$

Step 3.2.3

Cancel the common factor.

$\frac{x (9 x y^{3})}{x \cdot 1}$

Step 3.2.4

Rewrite the expression.

$\frac{9 x y^{3}}{1}$

Step 3.2.5

Divide $9 x y^{3}$ by $1$ .

$9 x y^{3}$

$9 x y^{3}$

$9 x y^{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$