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

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

Step 1

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

Factor out $y^{2}$ .

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

Reorder $x$ and $y^{2}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

Step 4

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

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

Step 5

Multiply $y$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

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

Multiply $y^{2}$ by $y$ .

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

$y^{2} y^{1} \sqrt{x y} \cdot x$

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

$y^{2 + 1} \sqrt{x y} \cdot x$

Add $2$ and $1$ .

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

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