Simplify fourth root of x^(2a)n^8

$\sqrt[4]{x^{2 a} n^{8}}$

Step 1

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

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

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

Reorder $x^{2 a}$ and ${(n^{2})}^{4}$ .

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

Step 2

Pull terms out from under the radical.

$n^{2} \sqrt[4]{x^{2 a}}$

Step 3

Rewrite $x^{2 a}$ as ${(x^{a})}^{2}$ .

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

Step 4

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

$n^{2} \sqrt{\sqrt{{(x^{a})}^{2}}}$

Step 5

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

$n^{2} \sqrt{x^{a}}$