Simplify fourth root of 128x^8

$\sqrt[4]{128 x^{8}}$

Step 1

Rewrite $128 x^{8}$ as ${(2 x^{2})}^{4} \cdot 8$ .

Factor $16$ out of $128$ .

$\sqrt[4]{16 (8) x^{8}}$

Rewrite $16$ as $2^{4}$ .

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

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

$\sqrt[4]{2^{4} \cdot 8 {(x^{2})}^{4}}$

Move $8$ .

$\sqrt[4]{2^{4} {(x^{2})}^{4} \cdot 8}$

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

$\sqrt[4]{{(2 x^{2})}^{4} \cdot 8}$

Step 2

Pull terms out from under the radical.

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