Simplify the Radical Expression square root of (a^8)/(b^12)

$\sqrt{\frac{a^{8}}{b^{12}}}$

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

$\sqrt{\frac{{(a^{4})}^{2}}{b^{12}}}$

Rewrite $b^{12}$ as ${(b^{6})}^{2}$ .

$\sqrt{\frac{{(a^{4})}^{2}}{{(b^{6})}^{2}}}$

Rewrite $\frac{{(a^{4})}^{2}}{{(b^{6})}^{2}}$ as ${(\frac{a^{4}}{b^{6}})}^{2}$ .

$\sqrt{{(\frac{a^{4}}{b^{6}})}^{2}}$

Pull terms out from under the radical.

$| \frac{a^{4}}{b^{6}} |$

Remove non-negative terms from the absolute value.

$\frac{a^{4}}{b^{6}}$