Simplify the Radical Expression fourth root of (81x^2y^4)/(z^8)

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

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

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

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

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

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

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

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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

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

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

Pull terms out from under the radical.

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

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

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