Algebra Examples

$\sqrt[8]{\frac{n^{7}}{n^{5}}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Reduce the expression $\frac{n^{7}}{n^{5}}$ by cancelling the common factors.

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Step 1.1.1

Factor $n^{5}$ out of $n^{7}$ .

$\sqrt[8]{\frac{n^{5} n^{2}}{n^{5}}}$

Step 1.1.2

Multiply by $1$ .

$\sqrt[8]{\frac{n^{5} n^{2}}{n^{5} \cdot 1}}$

Step 1.1.3

Cancel the common factor.

$\sqrt[8]{\frac{n^{5} n^{2}}{n^{5} \cdot 1}}$

Step 1.1.4

Rewrite the expression.

$\sqrt[8]{\frac{n^{2}}{1}}$

Step 1.2

Divide $n^{2}$ by $1$ .

$\sqrt[8]{n^{2}}$

Step 2

Rewrite $\sqrt[8]{n^{2}}$ as $\sqrt[4]{\sqrt{n^{2}}}$ .

$\sqrt[4]{\sqrt{n^{2}}}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt[4]{n}$