Simplify cube root of 2* cube root of 4

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

Combine using the product rule for radicals.

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

Write the expression using exponents.

Multiply $2$ by $4$ .

$\sqrt[3]{8}$

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

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

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

$2$