Algebra Examples

$\frac{14}{\sqrt{4 x^{3}}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $4 x^{3}$ as ${(2 x)}^{2} x$ .

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Step 1.1.1

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

$\frac{14}{\sqrt{2^{2} x^{3}}}$

Step 1.1.2

Factor out $x^{2}$ .

$\frac{14}{\sqrt{2^{2} (x^{2} x)}}$

Step 1.1.3

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

$\frac{14}{\sqrt{{(2 x)}^{2} x}}$

Step 1.2

Pull terms out from under the radical.

$\frac{14}{2 x \sqrt{x}}$

Step 2

Cancel the common factor of $14$ and $2$ .

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Step 2.1

Factor $2$ out of $14$ .

$\frac{2 \cdot 7}{2 x \sqrt{x}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{2 \cdot 7}{2 (x \sqrt{x})}$

Step 2.2.2

Cancel the common factor.

$\frac{2 \cdot 7}{2 (x \sqrt{x})}$

Step 2.2.3

Rewrite the expression.

$\frac{7}{x \sqrt{x}}$

Step 3

Multiply $\frac{7}{x \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{7}{x \sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{7}{x \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{7 \sqrt{x}}{x \sqrt{x} \sqrt{x}}$

Step 4.2

Move $\sqrt{x}$ .

$\frac{7 \sqrt{x}}{x (\sqrt{x} \sqrt{x})}$

Step 4.3

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

$\frac{7 \sqrt{x}}{x ({\sqrt{x}}^{1} \sqrt{x})}$

Step 4.4

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

$\frac{7 \sqrt{x}}{x ({\sqrt{x}}^{1} {\sqrt{x}}^{1})}$

Step 4.5

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

$\frac{7 \sqrt{x}}{x {\sqrt{x}}^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$\frac{7 \sqrt{x}}{x {\sqrt{x}}^{2}}$

Step 4.7

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

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Step 4.7.1

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

$\frac{7 \sqrt{x}}{x {(x^{\frac{1}{2}})}^{2}}$

Step 4.7.2

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

$\frac{7 \sqrt{x}}{x \cdot x^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

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

$\frac{7 \sqrt{x}}{x \cdot x^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

$\frac{7 \sqrt{x}}{x \cdot x^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{7 \sqrt{x}}{x \cdot x^{1}}$

Step 4.7.5

Simplify.

$\frac{7 \sqrt{x}}{x \cdot x}$

Step 5

Multiply $x$ by $x$ .

$\frac{7 \sqrt{x}}{x^{2}}$