Algebra Examples

$\sqrt[2 n]{x^{6 n}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[2 n]{x^{6 n}}$ as $x^{\frac{6 n}{2 n}}$ .

$x^{\frac{6 n}{2 n}}$

Step 2

Cancel the common factor of $6$ and $2$ .

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Step 2.1

Factor $2$ out of $6 n$ .

$x^{\frac{2 (3 n)}{2 n}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2 n$ .

$x^{\frac{2 (3 n)}{2 (n)}}$

Step 2.2.2

Cancel the common factor.

$x^{\frac{2 (3 n)}{2 n}}$

Step 2.2.3

Rewrite the expression.

$x^{\frac{3 n}{n}}$

Step 3

Cancel the common factor of $n$ .

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Step 3.1

Cancel the common factor.

$x^{\frac{3 n}{n}}$

Step 3.2

Divide $3$ by $1$ .

$x^{3}$