Pre-Algebra Examples

$\frac{8}{\sqrt[7]{x^{15}}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $x^{15}$ as ${(x^{2})}^{7} x$ .

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Step 1.1.1

Factor out $x^{14}$ .

$\frac{8}{\sqrt[7]{x^{14} x}}$

Step 1.1.2

Rewrite $x^{14}$ as ${(x^{2})}^{7}$ .

$\frac{8}{\sqrt[7]{{(x^{2})}^{7} x}}$

Step 1.2

Pull terms out from under the radical.

$\frac{8}{x^{2} \sqrt[7]{x}}$

Step 2

Multiply $\frac{8}{x^{2} \sqrt[7]{x}}$ by $\frac{{\sqrt[7]{x}}^{6}}{{\sqrt[7]{x}}^{6}}$ .

$\frac{8}{x^{2} \sqrt[7]{x}} \cdot \frac{{\sqrt[7]{x}}^{6}}{{\sqrt[7]{x}}^{6}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{8}{x^{2} \sqrt[7]{x}}$ by $\frac{{\sqrt[7]{x}}^{6}}{{\sqrt[7]{x}}^{6}}$ .

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} \sqrt[7]{x} {\sqrt[7]{x}}^{6}}$

Step 3.2

Move $\sqrt[7]{x}$ .

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} (\sqrt[7]{x} {\sqrt[7]{x}}^{6})}$

Step 3.3

Raise $\sqrt[7]{x}$ to the power of $1$ .

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} ({\sqrt[7]{x}}^{1} {\sqrt[7]{x}}^{6})}$

Step 3.4

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

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} {\sqrt[7]{x}}^{1 + 6}}$

Step 3.5

Add $1$ and $6$ .

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} {\sqrt[7]{x}}^{7}}$

Step 3.6

Rewrite ${\sqrt[7]{x}}^{7}$ as $x$ .

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Step 3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[7]{x}$ as $x^{\frac{1}{7}}$ .

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} {(x^{\frac{1}{7}})}^{7}}$

Step 3.6.2

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

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} x^{\frac{1}{7} \cdot 7}}$

Step 3.6.3

Combine $\frac{1}{7}$ and $7$ .

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} x^{\frac{7}{7}}}$

Step 3.6.4

Cancel the common factor of $7$ .

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Step 3.6.4.1

Cancel the common factor.

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} x^{\frac{7}{7}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} x^{1}}$

Step 3.6.5

Simplify.

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} x}$

Step 4

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 4.1

Multiply $x^{2}$ by $x$ .

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Step 4.1.1

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

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2} x^{1}}$

Step 4.1.2

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

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{2 + 1}}$

Step 4.2

Add $2$ and $1$ .

$\frac{8 {\sqrt[7]{x}}^{6}}{x^{3}}$

Step 5

Rewrite ${\sqrt[7]{x}}^{6}$ as $\sqrt[7]{x^{6}}$ .

$\frac{8 \sqrt[7]{x^{6}}}{x^{3}}$