Simplify the Radical Expression cube root of 432x^3

$\sqrt[3]{432 x^{3}}$

Rewrite $432 x^{3}$ as ${(6 x)}^{3} \cdot 2$ .

Factor $216$ out of $432$ .

$\sqrt[3]{216 (2) x^{3}}$

Rewrite $216$ as $6^{3}$ .

$\sqrt[3]{6^{3} \cdot 2 x^{3}}$

Move $2$ .

$\sqrt[3]{6^{3} x^{3} \cdot 2}$

Rewrite $6^{3} x^{3}$ as ${(6 x)}^{3}$ .

$\sqrt[3]{{(6 x)}^{3} \cdot 2}$

Pull terms out from under the radical.

$6 x \sqrt[3]{2}$