Precalculus Examples

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

Step 1

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

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Step 1.1

Factor out $y^{2}$ .

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

Step 1.2

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

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

Step 1.3

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Move $y$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $1$ and $2$ .

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

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