Algebra Examples

$\sqrt[4]{\frac{81 x^{2} y^{4}}{z^{8}}}$

Step 1

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

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Step 1.1

Factor the perfect power ${(3 y)}^{4}$ out of $81 x^{2} y^{4}$ .

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

Step 1.2

Factor the perfect power ${(z^{2})}^{4}$ out of $z^{8}$ .

$\sqrt[4]{\frac{{(3 y)}^{4} x^{2}}{{(z^{2})}^{4} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{{(3 y)}^{4} x^{2}}{{(z^{2})}^{4} \cdot 1}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

Step 4

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

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

Step 5

Combine $\frac{3 y}{z^{2}}$ and $\sqrt{x}$ .

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