Algebra Examples

$\sqrt[8]{x^{6} y^{12}}$

Step 1

Rewrite $x^{6} y^{12}$ as $y^{8} (x^{6} y^{4})$ .

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Step 1.1

Factor out $y^{8}$ .

$\sqrt[8]{x^{6} (y^{8} y^{4})}$

Step 1.2

Reorder $x^{6}$ and $y^{8}$ .

$\sqrt[8]{y^{8} x^{6} y^{4}}$

Step 1.3

Add parentheses.

$\sqrt[8]{y^{8} (x^{6} y^{4})}$

Step 2

Pull terms out from under the radical.

$y \sqrt[8]{x^{6} y^{4}}$

Step 3

Rewrite $x^{6} y^{4}$ as ${(x^{3} y^{2})}^{2}$ .

$y \sqrt[8]{{(x^{3} y^{2})}^{2}}$

Step 4

Rewrite $\sqrt[8]{{(x^{3} y^{2})}^{2}}$ as $\sqrt[4]{\sqrt{{(x^{3} y^{2})}^{2}}}$ .

$y \sqrt[4]{\sqrt{{(x^{3} y^{2})}^{2}}}$

Step 5

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

$y \sqrt[4]{x^{3} y^{2}}$