Simplify cube root of 216x^4y^3

$\sqrt[3]{216 x^{4} y^{3}}$

Step 1

Rewrite $216 x^{4} y^{3}$ as ${(6 x y)}^{3} x$ .

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

$\sqrt[3]{6^{3} x^{4} y^{3}}$

Factor out $x^{3}$ .

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

Move $x$ .

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

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

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

Step 2

Pull terms out from under the radical.

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