Simplify eighth root of 81a^(4n)

$\sqrt[8]{81 a^{4 n}}$

Step 1

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

$\sqrt[8]{{(3 a^{n})}^{4}}$

Step 2

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

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

Step 3

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

$\sqrt{3 a^{n}}$