Simplify fourth root of (a^4)/(b^8)

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

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

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

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

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

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

$\frac{a}{b^{2}}$