Simplify eighth root of a^6

$\sqrt[8]{a^{6}}$

Step 1

Rewrite $a^{6}$ as ${(a^{3})}^{2}$ .

$\sqrt[8]{{(a^{3})}^{2}}$

Step 2

Rewrite $\sqrt[8]{{(a^{3})}^{2}}$ as $\sqrt[4]{\sqrt{{(a^{3})}^{2}}}$ .

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

Step 3

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

$\sqrt[4]{a^{3}}$