Simplify 2 cube root of 4*2 cube root of 2

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

Step 1

Multiply $2 \sqrt[3]{4} (2 \sqrt[3]{2})$ .

Multiply $2$ by $2$ .

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

Combine using the product rule for radicals.

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

Multiply $2$ by $4$ .

$4 \sqrt[3]{8}$

Step 2

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

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

Step 3

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

$4 \cdot 2$

Step 4

Multiply $4$ by $2$ .

$8$