Algebra Examples

$\frac{\sqrt[7]{14 x^{6}}}{\sqrt[7]{2 x^{5}}}$

Step 1

Combine $\sqrt[7]{14 x^{6}}$ and $\sqrt[7]{2 x^{5}}$ into a single radical.

$\sqrt[7]{\frac{14 x^{6}}{2 x^{5}}}$

Step 2

Reduce the expression $\frac{14 x^{6}}{2 x^{5}}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $14 x^{6}$ .

$\sqrt[7]{\frac{2 (7 x^{6})}{2 x^{5}}}$

Step 2.2

Factor $2$ out of $2 x^{5}$ .

$\sqrt[7]{\frac{2 (7 x^{6})}{2 (x^{5})}}$

Step 2.3

Cancel the common factor.

$\sqrt[7]{\frac{2 (7 x^{6})}{2 x^{5}}}$

Step 2.4

Rewrite the expression.

$\sqrt[7]{\frac{7 x^{6}}{x^{5}}}$

Step 3

Cancel the common factor of $x^{6}$ and $x^{5}$ .

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Step 3.1

Factor $x^{5}$ out of $7 x^{6}$ .

$\sqrt[7]{\frac{x^{5} (7 x)}{x^{5}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\sqrt[7]{\frac{x^{5} (7 x)}{x^{5} \cdot 1}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[7]{\frac{x^{5} (7 x)}{x^{5} \cdot 1}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[7]{\frac{7 x}{1}}$

Step 3.2.4

Divide $7 x$ by $1$ .

$\sqrt[7]{7 x}$