Algebra Examples

$\frac{6}{\sqrt{20 a^{4}}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $20 a^{4}$ as ${(2 a^{2})}^{2} \cdot 5$ .

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Step 1.1.1

Factor $4$ out of $20$ .

$\frac{6}{\sqrt{4 (5) a^{4}}}$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$\frac{6}{\sqrt{2^{2} \cdot 5 a^{4}}}$

Step 1.1.3

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

$\frac{6}{\sqrt{2^{2} \cdot 5 {(a^{2})}^{2}}}$

Step 1.1.4

Move $5$ .

$\frac{6}{\sqrt{2^{2} {(a^{2})}^{2} \cdot 5}}$

Step 1.1.5

Rewrite $2^{2} {(a^{2})}^{2}$ as ${(2 a^{2})}^{2}$ .

$\frac{6}{\sqrt{{(2 a^{2})}^{2} \cdot 5}}$

Step 1.2

Pull terms out from under the radical.

$\frac{6}{2 a^{2} \sqrt{5}}$

Step 2

Cancel the common factor of $6$ and $2$ .

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Step 2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 3}{2 a^{2} \sqrt{5}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2 a^{2} \sqrt{5}$ .

$\frac{2 \cdot 3}{2 (a^{2} \sqrt{5})}$

Step 2.2.2

Cancel the common factor.

$\frac{2 \cdot 3}{2 (a^{2} \sqrt{5})}$

Step 2.2.3

Rewrite the expression.

$\frac{3}{a^{2} \sqrt{5}}$

Step 3

Multiply $\frac{3}{a^{2} \sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{3}{a^{2} \sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{3}{a^{2} \sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{3 \sqrt{5}}{a^{2} \sqrt{5} \sqrt{5}}$

Step 4.2

Move $\sqrt{5}$ .

$\frac{3 \sqrt{5}}{a^{2} (\sqrt{5} \sqrt{5})}$

Step 4.3

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{3 \sqrt{5}}{a^{2} ({\sqrt{5}}^{1} \sqrt{5})}$

Step 4.4

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{3 \sqrt{5}}{a^{2} ({\sqrt{5}}^{1} {\sqrt{5}}^{1})}$

Step 4.5

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

$\frac{3 \sqrt{5}}{a^{2} {\sqrt{5}}^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$\frac{3 \sqrt{5}}{a^{2} {\sqrt{5}}^{2}}$

Step 4.7

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 4.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{3 \sqrt{5}}{a^{2} {(5^{\frac{1}{2}})}^{2}}$

Step 4.7.2

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

$\frac{3 \sqrt{5}}{a^{2} \cdot 5^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

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

$\frac{3 \sqrt{5}}{a^{2} \cdot 5^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

$\frac{3 \sqrt{5}}{a^{2} \cdot 5^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{3 \sqrt{5}}{a^{2} \cdot 5^{1}}$

Step 4.7.5

Evaluate the exponent.

$\frac{3 \sqrt{5}}{a^{2} \cdot 5}$

Step 5

Move $5$ to the left of $a^{2}$ .

$\frac{3 \sqrt{5}}{5 a^{2}}$