Simplify 2x^3 square root of 4x^2y^2

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

Step 1

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

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

Step 2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 3

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $3$ .

$2 x^{4} (2 y)$

Step 4

Rewrite using the commutative property of multiplication.

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

Step 5

Multiply $2$ by $2$ .

$4 x^{4} y$