Algebra Examples

$\frac{12 w^{9} v^{4}}{{(4 w v)}^{2}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $4 w v$ .

$\frac{12 w^{9} v^{4}}{{(4 w)}^{2} v^{2}}$

Step 1.2

Apply the product rule to $4 w$ .

$\frac{12 w^{9} v^{4}}{4^{2} w^{2} v^{2}}$

Step 1.3

Raise $4$ to the power of $2$ .

$\frac{12 w^{9} v^{4}}{16 w^{2} v^{2}}$

$\frac{12 w^{9} v^{4}}{16 w^{2} v^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $12$ and $16$ .

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Step 2.1.1

Factor $4$ out of $12 w^{9} v^{4}$ .

$\frac{4 (3 w^{9} v^{4})}{16 w^{2} v^{2}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $4$ out of $16 w^{2} v^{2}$ .

$\frac{4 (3 w^{9} v^{4})}{4 (4 w^{2} v^{2})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{4 (3 w^{9} v^{4})}{4 (4 w^{2} v^{2})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{3 w^{9} v^{4}}{4 w^{2} v^{2}}$

$\frac{3 w^{9} v^{4}}{4 w^{2} v^{2}}$

$\frac{3 w^{9} v^{4}}{4 w^{2} v^{2}}$

Step 2.2

Cancel the common factor of $w^{9}$ and $w^{2}$ .

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Step 2.2.1

Factor $w^{2}$ out of $3 w^{9} v^{4}$ .

$\frac{w^{2} (3 w^{7} v^{4})}{4 w^{2} v^{2}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $w^{2}$ out of $4 w^{2} v^{2}$ .

$\frac{w^{2} (3 w^{7} v^{4})}{w^{2} (4 v^{2})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{w^{2} (3 w^{7} v^{4})}{w^{2} (4 v^{2})}$

Step 2.2.2.3

Rewrite the expression.

$\frac{3 w^{7} v^{4}}{4 v^{2}}$

$\frac{3 w^{7} v^{4}}{4 v^{2}}$

$\frac{3 w^{7} v^{4}}{4 v^{2}}$

Step 2.3

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

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Step 2.3.1

Factor $v^{2}$ out of $3 w^{7} v^{4}$ .

$\frac{v^{2} (3 w^{7} v^{2})}{4 v^{2}}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $v^{2}$ out of $4 v^{2}$ .

$\frac{v^{2} (3 w^{7} v^{2})}{v^{2} \cdot 4}$

Step 2.3.2.2

Cancel the common factor.

$\frac{v^{2} (3 w^{7} v^{2})}{v^{2} \cdot 4}$

Step 2.3.2.3

Rewrite the expression.

$\frac{3 w^{7} v^{2}}{4}$

$\frac{3 w^{7} v^{2}}{4}$

$\frac{3 w^{7} v^{2}}{4}$

$\frac{3 w^{7} v^{2}}{4}$

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