Finite Math Examples

$\sqrt[7]{\frac{4 x^{30}}{486 x^{8}}}$

Step 1

Reduce the expression $\frac{4 x^{30}}{486 x^{8}}$ by cancelling the common factors.

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Step 1.1

Factor $2$ out of $4 x^{30}$ .

$\sqrt[7]{\frac{2 (2 x^{30})}{486 x^{8}}}$

Step 1.2

Factor $2$ out of $486 x^{8}$ .

$\sqrt[7]{\frac{2 (2 x^{30})}{2 (243 x^{8})}}$

Step 1.3

Cancel the common factor.

$\sqrt[7]{\frac{2 (2 x^{30})}{2 (243 x^{8})}}$

Step 1.4

Rewrite the expression.

$\sqrt[7]{\frac{2 x^{30}}{243 x^{8}}}$

Step 2

Cancel the common factor of $x^{30}$ and $x^{8}$ .

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Step 2.1

Factor $x^{8}$ out of $2 x^{30}$ .

$\sqrt[7]{\frac{x^{8} (2 x^{22})}{243 x^{8}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x^{8}$ out of $243 x^{8}$ .

$\sqrt[7]{\frac{x^{8} (2 x^{22})}{x^{8} \cdot 243}}$

Step 2.2.2

Cancel the common factor.

$\sqrt[7]{\frac{x^{8} (2 x^{22})}{x^{8} \cdot 243}}$

Step 2.2.3

Rewrite the expression.

$\sqrt[7]{\frac{2 x^{22}}{243}}$

Step 3

Rewrite $\sqrt[7]{\frac{2 x^{22}}{243}}$ as $\frac{\sqrt[7]{2 x^{22}}}{\sqrt[7]{243}}$ .

$\frac{\sqrt[7]{2 x^{22}}}{\sqrt[7]{243}}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite $2 x^{22}$ as ${(x^{3})}^{7} \cdot (2 x)$ .

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Step 4.1.1

Factor out $x^{21}$ .

$\frac{\sqrt[7]{2 (x^{21} x)}}{\sqrt[7]{243}}$

Step 4.1.2

Rewrite $x^{21}$ as ${(x^{3})}^{7}$ .

$\frac{\sqrt[7]{2 ({(x^{3})}^{7} x)}}{\sqrt[7]{243}}$

Step 4.1.3

Reorder $2$ and ${(x^{3})}^{7}$ .

$\frac{\sqrt[7]{{(x^{3})}^{7} \cdot 2 x}}{\sqrt[7]{243}}$

Step 4.1.4

Add parentheses.

$\frac{\sqrt[7]{{(x^{3})}^{7} \cdot (2 x)}}{\sqrt[7]{243}}$

Step 4.2

Pull terms out from under the radical.

$\frac{x^{3} \sqrt[7]{2 x}}{\sqrt[7]{243}}$