Simplify 2x^3y^3 square root of 18x^3y^2

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

Rewrite $18 x^{3} y^{2}$ as ${(3 x y)}^{2} \cdot (2 x)$ .

Factor $9$ out of $18$ .

$2 x^{3} y^{3} \sqrt{9 (2) x^{3} y^{2}}$

Rewrite $9$ as $3^{2}$ .

$2 x^{3} y^{3} \sqrt{3^{2} \cdot 2 x^{3} y^{2}}$

Factor out $x^{2}$ .

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$2 (x^{1} x^{3}) y^{3} (3 y \sqrt{2 x})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 x^{1 + 3} y^{3} (3 y \sqrt{2 x})$

Add $1$ and $3$ .

$2 x^{4} y^{3} (3 y \sqrt{2 x})$

Multiply $y^{3}$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y^{3}$ .

Raise $y$ to the power of $1$ .

$2 x^{4} (y^{1} y^{3}) (3 \sqrt{2 x})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 x^{4} y^{1 + 3} (3 \sqrt{2 x})$

Add $1$ and $3$ .

$2 x^{4} y^{4} (3 \sqrt{2 x})$

Multiply $3$ by $2$ .

$6 x^{4} y^{4} \sqrt{2 x}$