Simplify fourth root of 64x^8

$\sqrt[4]{64 x^{8}}$

Step 1

Rewrite $64 x^{8}$ as ${(2 x^{2})}^{4} \cdot 4$ .

Factor $16$ out of $64$ .

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

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

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

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

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

Move $4$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

Step 4

Rewrite $\sqrt[4]{2^{2}}$ as $\sqrt{\sqrt{2^{2}}}$ .

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

Step 5

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

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