Algebra Examples

$\frac{\sqrt{2 x^{7}}}{8}$

Step 1

Multiply to rationalize the numerator.

$\frac{\sqrt{2 x^{7}} \sqrt{2 x^{7}}}{8 \sqrt{2 x^{7}}}$

Step 2

Simplify.

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Step 2.1

Raise $\sqrt{2 x^{7}}$ to the power of $1$ .

$\frac{{\sqrt{2 x^{7}}}^{1} \sqrt{2 x^{7}}}{8 \sqrt{2 x^{7}}}$

Step 2.2

Raise $\sqrt{2 x^{7}}$ to the power of $1$ .

$\frac{{\sqrt{2 x^{7}}}^{1} {\sqrt{2 x^{7}}}^{1}}{8 \sqrt{2 x^{7}}}$

Step 2.3

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

$\frac{{\sqrt{2 x^{7}}}^{1 + 1}}{8 \sqrt{2 x^{7}}}$

Step 2.4

Add $1$ and $1$ .

$\frac{{\sqrt{2 x^{7}}}^{2}}{8 \sqrt{2 x^{7}}}$

Step 2.5

Rewrite ${\sqrt{2 x^{7}}}^{2}$ as $2 x^{7}$ .

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Step 2.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x^{7}}$ as ${(2 x^{7})}^{\frac{1}{2}}$ .

$\frac{{({(2 x^{7})}^{\frac{1}{2}})}^{2}}{8 \sqrt{2 x^{7}}}$

Step 2.5.2

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

$\frac{{(2 x^{7})}^{\frac{1}{2} \cdot 2}}{8 \sqrt{2 x^{7}}}$

Step 2.5.3

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

$\frac{{(2 x^{7})}^{\frac{2}{2}}}{8 \sqrt{2 x^{7}}}$

Step 2.5.4

Cancel the common factor of $2$ .

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Step 2.5.4.1

Cancel the common factor.

$\frac{{(2 x^{7})}^{\frac{2}{2}}}{8 \sqrt{2 x^{7}}}$

Step 2.5.4.2

Rewrite the expression.

$\frac{{(2 x^{7})}^{1}}{8 \sqrt{2 x^{7}}}$

Step 2.5.5

Simplify.

$\frac{2 x^{7}}{8 \sqrt{2 x^{7}}}$

Step 2.6

Rewrite $2 x^{7}$ as ${(x^{3})}^{2} \cdot (2 x)$ .

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Step 2.6.1

Factor out $x^{6}$ .

$\frac{2 x^{7}}{8 \sqrt{2 (x^{6} x)}}$

Step 2.6.2

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

$\frac{2 x^{7}}{8 \sqrt{2 ({(x^{3})}^{2} x)}}$

Step 2.6.3

Reorder $2$ and ${(x^{3})}^{2}$ .

$\frac{2 x^{7}}{8 \sqrt{{(x^{3})}^{2} \cdot 2 x}}$

Step 2.6.4

Add parentheses.

$\frac{2 x^{7}}{8 \sqrt{{(x^{3})}^{2} \cdot (2 x)}}$

Step 2.7

Pull terms out from under the radical.

$\frac{2 x^{7}}{8 x^{3} \sqrt{2 x}}$