Finite Math Examples

$\frac{4 x^{8} w}{\sqrt{9 x w^{2}}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $9 x w^{2}$ as ${(3 w)}^{2} x$ .

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Step 1.1.1

Rewrite $9$ as $3^{2}$ .

$\frac{4 x^{8} w}{\sqrt{3^{2} x w^{2}}}$

Step 1.1.2

Move $x$ .

$\frac{4 x^{8} w}{\sqrt{3^{2} w^{2} x}}$

Step 1.1.3

Rewrite $3^{2} w^{2}$ as ${(3 w)}^{2}$ .

$\frac{4 x^{8} w}{\sqrt{{(3 w)}^{2} x}}$

Step 1.2

Pull terms out from under the radical.

$\frac{4 x^{8} w}{3 w \sqrt{x}}$

Step 2

Cancel the common factor of $w$ .

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Step 2.1

Cancel the common factor.

$\frac{4 x^{8} w}{3 w \sqrt{x}}$

Step 2.2

Rewrite the expression.

$\frac{4 x^{8}}{3 \sqrt{x}}$

Step 3

Multiply $\frac{4 x^{8}}{3 \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{4 x^{8}}{3 \sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{4 x^{8}}{3 \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{4 x^{8} \sqrt{x}}{3 \sqrt{x} \sqrt{x}}$

Step 4.2

Move $\sqrt{x}$ .

$\frac{4 x^{8} \sqrt{x}}{3 (\sqrt{x} \sqrt{x})}$

Step 4.3

Raise $\sqrt{x}$ to the power of $1$ .

$\frac{4 x^{8} \sqrt{x}}{3 ({\sqrt{x}}^{1} \sqrt{x})}$

Step 4.4

Raise $\sqrt{x}$ to the power of $1$ .

$\frac{4 x^{8} \sqrt{x}}{3 ({\sqrt{x}}^{1} {\sqrt{x}}^{1})}$

Step 4.5

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

$\frac{4 x^{8} \sqrt{x}}{3 {\sqrt{x}}^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$\frac{4 x^{8} \sqrt{x}}{3 {\sqrt{x}}^{2}}$

Step 4.7

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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Step 4.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\frac{4 x^{8} \sqrt{x}}{3 {(x^{\frac{1}{2}})}^{2}}$

Step 4.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4 x^{8} \sqrt{x}}{3 x^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{4 x^{8} \sqrt{x}}{3 x^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

$\frac{4 x^{8} \sqrt{x}}{3 x^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{4 x^{8} \sqrt{x}}{3 x^{1}}$

Step 4.7.5

Simplify.

$\frac{4 x^{8} \sqrt{x}}{3 x}$

Step 5

Cancel the common factor of $x^{8}$ and $x$ .

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Step 5.1

Factor $x$ out of $4 x^{8} \sqrt{x}$ .

$\frac{x (4 x^{7} \sqrt{x})}{3 x}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x$ out of $3 x$ .

$\frac{x (4 x^{7} \sqrt{x})}{x \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{x (4 x^{7} \sqrt{x})}{x \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{4 x^{7} \sqrt{x}}{3}$