Simplify the Radical Expression fourth root of (81a^12)/(625b^8)

$\sqrt[4]{\frac{81 a^{12}}{625 b^{8}}}$

Rewrite $81 a^{12}$ as ${(3 a^{3})}^{4}$ .

$\sqrt[4]{\frac{{(3 a^{3})}^{4}}{625 b^{8}}}$

Rewrite $625 b^{8}$ as ${(5 b^{2})}^{4}$ .

$\sqrt[4]{\frac{{(3 a^{3})}^{4}}{{(5 b^{2})}^{4}}}$

Rewrite $\frac{{(3 a^{3})}^{4}}{{(5 b^{2})}^{4}}$ as ${(\frac{3 a^{3}}{5 b^{2}})}^{4}$ .

$\sqrt[4]{{(\frac{3 a^{3}}{5 b^{2}})}^{4}}$

Pull terms out from under the radical.

$| \frac{3 a^{3}}{5 b^{2}} |$

Remove non-negative terms from the absolute value.

$\frac{3 | a^{3} |}{5 b^{2}}$