Algebra Examples

$\sqrt[4]{81 x^{6} y^{8}}$

Step 1

Rewrite $81 x^{6} y^{8}$ as ${(3 x y^{2})}^{4} x^{2}$ .

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Step 1.1

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} x^{6} y^{8}}$

Step 1.2

Factor out $x^{4}$ .

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

Step 1.3

Rewrite $y^{8}$ as ${(y^{2})}^{4}$ .

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

Step 1.4

Move $x^{2}$ .

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

Step 1.5

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

$3 x y^{2} \sqrt{\sqrt{x^{2}}}$

Step 4

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

$3 x y^{2} \sqrt{x}$