Algebra Examples

$\sqrt[4]{\frac{16}{x^{14}}}$

Step 1

Rewrite $\frac{16}{x^{14}}$ as ${(\frac{2}{x^{3}})}^{4} \frac{1}{x^{2}}$ .

Tap for more steps...

Step 1.1

Factor the perfect power $2^{4}$ out of $16$ .

$\sqrt[4]{\frac{2^{4} \cdot 1}{x^{14}}}$

Step 1.2

Factor the perfect power ${(x^{3})}^{4}$ out of $x^{14}$ .

$\sqrt[4]{\frac{2^{4} \cdot 1}{{(x^{3})}^{4} x^{2}}}$

Step 1.3

Rearrange the fraction $\frac{2^{4} \cdot 1}{{(x^{3})}^{4} x^{2}}$ .

$\sqrt[4]{{(\frac{2}{x^{3}})}^{4} \frac{1}{x^{2}}}$

Step 2

Pull terms out from under the radical.

$\frac{2}{x^{3}} \sqrt[4]{\frac{1}{x^{2}}}$

Step 3

Rewrite $1$ as $1^{2}$ .

$\frac{2}{x^{3}} \sqrt[4]{\frac{1^{2}}{x^{2}}}$

Step 4

Rewrite $\frac{1^{2}}{x^{2}}$ as ${(\frac{1}{x})}^{2}$ .

$\frac{2}{x^{3}} \sqrt[4]{{(\frac{1}{x})}^{2}}$

Step 5

Rewrite $\sqrt[4]{{(\frac{1}{x})}^{2}}$ as $\sqrt{\sqrt{{(\frac{1}{x})}^{2}}}$ .

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

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$\frac{2}{x^{3}} \sqrt{\frac{1}{x}}$

Step 7

Rewrite $\sqrt{\frac{1}{x}}$ as $\frac{\sqrt{1}}{\sqrt{x}}$ .

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

Step 8

Combine.

$\frac{2 \sqrt{1}}{x^{3} \sqrt{x}}$

Step 9

Any root of $1$ is $1$ .

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

Step 10

Multiply $2$ by $1$ .

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

Step 11

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

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

Step 12

Combine and simplify the denominator.

Tap for more steps...

Step 12.1

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

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

Step 12.2

Move $\sqrt{x}$ .

$\frac{2 \sqrt{x}}{x^{3} (\sqrt{x} \sqrt{x})}$

Step 12.3

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

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

Step 12.4

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

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

Step 12.5

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

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

Step 12.6

Add $1$ and $1$ .

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

Step 12.7

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

Tap for more steps...

Step 12.7.1

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

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

Step 12.7.2

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

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

Step 12.7.3

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

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

Step 12.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 12.7.4.1

Cancel the common factor.

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

Step 12.7.4.2

Rewrite the expression.

$\frac{2 \sqrt{x}}{x^{3} x^{1}}$

Step 12.7.5

Simplify.

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

Step 13

Multiply $x^{3}$ by $x$ by adding the exponents.

Tap for more steps...

Step 13.1

Multiply $x^{3}$ by $x$ .

Tap for more steps...

Step 13.1.1

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

$\frac{2 \sqrt{x}}{x^{3} x^{1}}$

Step 13.1.2

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

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

Step 13.2

Add $3$ and $1$ .

$\frac{2 \sqrt{x}}{x^{4}}$