Simplify cube root of 4x^2* cube root of 8x^3

$\sqrt[3]{4 x^{2}} \cdot \sqrt[3]{8 x^{3}}$

Rewrite $8 x^{3}$ as ${(2 x)}^{3}$ .

$\sqrt[3]{4 x^{2}} \cdot \sqrt[3]{{(2 x)}^{3}}$

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

$\sqrt[3]{4 x^{2}} \cdot (2 x)$

Rewrite using the commutative property of multiplication.

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