Simplify cube root of 4 sixth root of 64

$\sqrt[3]{4 \sqrt[6]{64}}$

Step 1

Rewrite $64$ as $2^{6}$ .

$\sqrt[3]{4 \sqrt[6]{2^{6}}}$

Step 2

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

$\sqrt[3]{4 \cdot 2}$

Step 3

Multiply $4$ by $2$ .

$\sqrt[3]{8}$

Step 4

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3}}$

Step 5

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

$2$