Algebra Examples

$\frac{2 q^{2}}{\sqrt{18 q^{6}}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $18 q^{6}$ as ${(3 q^{3})}^{2} \cdot 2$ .

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Step 1.1.1

Factor $9$ out of $18$ .

$\frac{2 q^{2}}{\sqrt{9 (2) q^{6}}}$

Step 1.1.2

Rewrite $9$ as $3^{2}$ .

$\frac{2 q^{2}}{\sqrt{3^{2} \cdot 2 q^{6}}}$

Step 1.1.3

Rewrite $q^{6}$ as ${(q^{3})}^{2}$ .

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

Step 1.1.4

Move $2$ .

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

Step 1.1.5

Rewrite $3^{2} {(q^{3})}^{2}$ as ${(3 q^{3})}^{2}$ .

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

Step 1.2

Pull terms out from under the radical.

$\frac{2 q^{2}}{3 q^{3} \sqrt{2}}$

Step 2

Cancel the common factor of $q^{2}$ and $q^{3}$ .

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Step 2.1

Factor $q^{2}$ out of $2 q^{2}$ .

$\frac{q^{2} \cdot 2}{3 q^{3} \sqrt{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $q^{2}$ out of $3 q^{3} \sqrt{2}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$\frac{2}{3 q \sqrt{2}}$

Step 3

Multiply $\frac{2}{3 q \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{2}{3 q \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{2}{3 q \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{2 \sqrt{2}}{3 q \sqrt{2} \sqrt{2}}$

Step 4.2

Move $\sqrt{2}$ .

$\frac{2 \sqrt{2}}{3 q (\sqrt{2} \sqrt{2})}$

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

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

$\frac{2 \sqrt{2}}{3 q {\sqrt{2}}^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$\frac{2 \sqrt{2}}{3 q {\sqrt{2}}^{2}}$

Step 4.7

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

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Step 4.7.1

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

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

Step 4.7.2

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

$\frac{2 \sqrt{2}}{3 q \cdot 2^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

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

$\frac{2 \sqrt{2}}{3 q \cdot 2^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

$\frac{2 \sqrt{2}}{3 q \cdot 2^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{2 \sqrt{2}}{3 q \cdot 2^{1}}$

Step 4.7.5

Evaluate the exponent.

$\frac{2 \sqrt{2}}{3 q \cdot 2}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$\frac{2 \sqrt{2}}{3 q \cdot 2}$

Step 5.2

Rewrite the expression.

$\frac{\sqrt{2}}{3 q}$