Simplify the Radical Expression (2 cube root of 2)(6 cube root of 4)

$(2 \sqrt[3]{2}) (6 \sqrt[3]{4})$

Step 1

Multiply $(2 \sqrt[3]{2}) (6 \sqrt[3]{4})$ .

Multiply $6$ by $2$ .

$12 \sqrt[3]{2} \sqrt[3]{4}$

Combine using the product rule for radicals.

$12 \sqrt[3]{4 \cdot 2}$

Multiply $4$ by $2$ .

$12 \sqrt[3]{8}$

Step 2

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

$12 \sqrt[3]{2^{3}}$

Step 3

Pull terms out from under the radical.

$12 \cdot 2$

Step 4

Multiply $12$ by $2$ .

$24$