Simplify the Radical Expression fourth root of (x^24z^12)/81

$\sqrt[4]{\frac{x^{24} z^{12}}{81}}$

Rewrite $x^{24} z^{12}$ as ${(x^{6} z^{3})}^{4}$ .

$\sqrt[4]{\frac{{(x^{6} z^{3})}^{4}}{81}}$

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

$\sqrt[4]{\frac{{(x^{6} z^{3})}^{4}}{3^{4}}}$

Rewrite $\frac{{(x^{6} z^{3})}^{4}}{3^{4}}$ as ${(\frac{x^{6} z^{3}}{3})}^{4}$ .

$\sqrt[4]{{(\frac{x^{6} z^{3}}{3})}^{4}}$

Pull terms out from under the radical.

$| \frac{x^{6} z^{3}}{3} |$

Remove non-negative terms from the absolute value.

$\frac{x^{6} | z^{3} |}{3}$