Algebra Examples

$\frac{8 a^{2} b^{2}}{2 \sqrt{2 b}}$

Step 1

Cancel the common factor of $8$ and $2$ .

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Step 1.1

Factor $2$ out of $8 a^{2} b^{2}$ .

$\frac{2 (4 a^{2} b^{2})}{2 \sqrt{2 b}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2 \sqrt{2 b}$ .

$\frac{2 (4 a^{2} b^{2})}{2 (\sqrt{2 b})}$

Step 1.2.2

Cancel the common factor.

$\frac{2 (4 a^{2} b^{2})}{2 \sqrt{2 b}}$

Step 1.2.3

Rewrite the expression.

$\frac{4 a^{2} b^{2}}{\sqrt{2 b}}$

Step 2

Multiply $\frac{4 a^{2} b^{2}}{\sqrt{2 b}}$ by $\frac{\sqrt{2 b}}{\sqrt{2 b}}$ .

$\frac{4 a^{2} b^{2}}{\sqrt{2 b}} \cdot \frac{\sqrt{2 b}}{\sqrt{2 b}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{4 a^{2} b^{2}}{\sqrt{2 b}}$ by $\frac{\sqrt{2 b}}{\sqrt{2 b}}$ .

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{\sqrt{2 b} \sqrt{2 b}}$

Step 3.2

Raise $\sqrt{2 b}$ to the power of $1$ .

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{{\sqrt{2 b}}^{1} \sqrt{2 b}}$

Step 3.3

Raise $\sqrt{2 b}$ to the power of $1$ .

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{{\sqrt{2 b}}^{1} {\sqrt{2 b}}^{1}}$

Step 3.4

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

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{{\sqrt{2 b}}^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{{\sqrt{2 b}}^{2}}$

Step 3.6

Rewrite ${\sqrt{2 b}}^{2}$ as $2 b$ .

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Step 3.6.1

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

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{{({(2 b)}^{\frac{1}{2}})}^{2}}$

Step 3.6.2

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

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{{(2 b)}^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

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

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{{(2 b)}^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{{(2 b)}^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{{(2 b)}^{1}}$

Step 3.6.5

Simplify.

$\frac{4 a^{2} b^{2} \sqrt{2 b}}{2 b}$

Step 4

Cancel the common factor of $4$ and $2$ .

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Step 4.1

Factor $2$ out of $4 a^{2} b^{2} \sqrt{2 b}$ .

$\frac{2 (2 a^{2} b^{2} \sqrt{2 b})}{2 b}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $2 b$ .

$\frac{2 (2 a^{2} b^{2} \sqrt{2 b})}{2 (b)}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (2 a^{2} b^{2} \sqrt{2 b})}{2 b}$

Step 4.2.3

Rewrite the expression.

$\frac{2 a^{2} b^{2} \sqrt{2 b}}{b}$

Step 5

Cancel the common factor of $b^{2}$ and $b$ .

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Step 5.1

Factor $b$ out of $2 a^{2} b^{2} \sqrt{2 b}$ .

$\frac{b (2 a^{2} b \sqrt{2 b})}{b}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{b (2 a^{2} b \sqrt{2 b})}{b^{1}}$

Step 5.2.2

Factor $b$ out of $b^{1}$ .

$\frac{b (2 a^{2} b \sqrt{2 b})}{b \cdot 1}$

Step 5.2.3

Cancel the common factor.

$\frac{b (2 a^{2} b \sqrt{2 b})}{b \cdot 1}$

Step 5.2.4

Rewrite the expression.

$\frac{2 a^{2} b \sqrt{2 b}}{1}$

Step 5.2.5

Divide $2 a^{2} b \sqrt{2 b}$ by $1$ .

$2 a^{2} b \sqrt{2 b}$