Pre-Algebra Examples

$(\sqrt{x y}) (\sqrt{x^{3} y^{5}})$

Step 1

Rewrite $x^{3} y^{5}$ as ${(x y^{2})}^{2} (x y)$ .

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Step 1.1

Factor out $x^{2}$ .

$\sqrt{x y} \sqrt{x^{2} x y^{5}}$

Step 1.2

Factor out $y^{4}$ .

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

Step 1.3

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

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

Step 1.4

Move $x$ .

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

Step 1.5

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

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

Step 1.6

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $\sqrt{x y} (x y^{2} \sqrt{x y})$ .

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Step 3.1

Raise $\sqrt{x y}$ to the power of $1$ .

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

Step 3.2

Raise $\sqrt{x y}$ to the power of $1$ .

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

Step 3.3

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

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

Step 3.4

Add $1$ and $1$ .

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

Step 4

Rewrite ${\sqrt{x y}}^{2}$ as $x y$ .

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x y}$ as ${(x y)}^{\frac{1}{2}}$ .

$x y^{2} {({(x y)}^{\frac{1}{2}})}^{2}$

Step 4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.3

Combine $\frac{1}{2}$ and $2$ .

$x y^{2} {(x y)}^{\frac{2}{2}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$x y^{2} {(x y)}^{\frac{2}{2}}$

Step 4.4.2

Rewrite the expression.

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

Step 4.5

Simplify.

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

Step 5

Multiply $x$ by $x$ by adding the exponents.

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Step 5.1

Move $x$ .

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

Step 5.2

Multiply $x$ by $x$ .

$x^{2} y^{2} y$

Step 6

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

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Step 6.1

Move $y$ .

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

Step 6.2

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

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Step 6.2.1

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

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

Step 6.2.2

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

$x^{2} y^{1 + 2}$

Step 6.3

Add $1$ and $2$ .

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