Simplify x^3y^3 square root of 4x^3y^3

$x^{3} y^{3} \sqrt{4 x^{3} y^{3}}$

Rewrite $4 x^{3} y^{3}$ as ${(2 x y)}^{2} (x y)$ .

Rewrite $4$ as $2^{2}$ .

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

Factor out $x^{2}$ .

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

Factor out $y^{2}$ .

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

Move $x$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $3$ .

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

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

Move $y$ .

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

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

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

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

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

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

Add $1$ and $3$ .

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