Simplify fourth root of 64a^4b^4

$\sqrt[4]{64 a^{4} b^{4}}$

Step 1

Rewrite $64 a^{4} b^{4}$ as ${(2 a b)}^{4} \cdot 4$ .

Factor $16$ out of $64$ .

$\sqrt[4]{16 (4) a^{4} b^{4}}$

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

$\sqrt[4]{2^{4} \cdot 4 a^{4} b^{4}}$

Move $4$ .

$\sqrt[4]{2^{4} a^{4} b^{4} \cdot 4}$

Rewrite $2^{4} a^{4} b^{4}$ as ${(2 a b)}^{4}$ .

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

Step 2

Pull terms out from under the radical.

$2 a b \sqrt[4]{4}$

Step 3

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

$2 a b \sqrt[4]{2^{2}}$

Step 4

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

$2 a b \sqrt{\sqrt{2^{2}}}$

Step 5

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

$2 a b \sqrt{2}$