Simplify the Radical Expression 3x cube root of 648x^4y^8

$3 x \sqrt[3]{648 x^{4} y^{8}}$

Step 1

Rewrite $648 x^{4} y^{8}$ as ${(6 x y^{2})}^{3} \cdot (3 x y^{2})$ .

Factor $216$ out of $648$ .

$3 x \sqrt[3]{216 (3) x^{4} y^{8}}$

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

$3 x \sqrt[3]{6^{3} \cdot 3 x^{4} y^{8}}$

Factor out $x^{3}$ .

$3 x \sqrt[3]{6^{3} \cdot 3 (x^{3} x) y^{8}}$

Factor out $y^{6}$ .

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

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

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

Move $x$ .

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

Move $3$ .

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

Rewrite $(6^{3} (x^{3})) {(y^{2})}^{3}$ as ${(6 x y^{2})}^{3}$ .

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Step 4

Multiply $6$ by $3$ .

$18 x^{2} (y^{2} \sqrt[3]{3 x y^{2}})$

Step 5

Reorder factors in $18 x^{2} (y^{2} \sqrt[3]{3 x y^{2}})$ .

$18 x^{2} y^{2} \sqrt[3]{3 x y^{2}}$