Algebra Examples

$\sqrt[6]{\frac{1}{2 s}}$

Step 1

Rewrite $\sqrt[6]{\frac{1}{2 s}}$ as $\frac{\sqrt[6]{1}}{\sqrt[6]{2 s}}$ .

$\frac{\sqrt[6]{1}}{\sqrt[6]{2 s}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[6]{2 s}}$

Step 3

Multiply $\frac{1}{\sqrt[6]{2 s}}$ by $\frac{{\sqrt[6]{2 s}}^{5}}{{\sqrt[6]{2 s}}^{5}}$ .

$\frac{1}{\sqrt[6]{2 s}} \cdot \frac{{\sqrt[6]{2 s}}^{5}}{{\sqrt[6]{2 s}}^{5}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{1}{\sqrt[6]{2 s}}$ by $\frac{{\sqrt[6]{2 s}}^{5}}{{\sqrt[6]{2 s}}^{5}}$ .

$\frac{{\sqrt[6]{2 s}}^{5}}{\sqrt[6]{2 s} {\sqrt[6]{2 s}}^{5}}$

Step 4.2

Raise $\sqrt[6]{2 s}$ to the power of $1$ .

$\frac{{\sqrt[6]{2 s}}^{5}}{{\sqrt[6]{2 s}}^{1} {\sqrt[6]{2 s}}^{5}}$

Step 4.3

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

$\frac{{\sqrt[6]{2 s}}^{5}}{{\sqrt[6]{2 s}}^{1 + 5}}$

Step 4.4

Add $1$ and $5$ .

$\frac{{\sqrt[6]{2 s}}^{5}}{{\sqrt[6]{2 s}}^{6}}$

Step 4.5

Rewrite ${\sqrt[6]{2 s}}^{6}$ as $2 s$ .

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Step 4.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{2 s}$ as ${(2 s)}^{\frac{1}{6}}$ .

$\frac{{\sqrt[6]{2 s}}^{5}}{{({(2 s)}^{\frac{1}{6}})}^{6}}$

Step 4.5.2

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

$\frac{{\sqrt[6]{2 s}}^{5}}{{(2 s)}^{\frac{1}{6} \cdot 6}}$

Step 4.5.3

Combine $\frac{1}{6}$ and $6$ .

$\frac{{\sqrt[6]{2 s}}^{5}}{{(2 s)}^{\frac{6}{6}}}$

Step 4.5.4

Cancel the common factor of $6$ .

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Step 4.5.4.1

Cancel the common factor.

$\frac{{\sqrt[6]{2 s}}^{5}}{{(2 s)}^{\frac{6}{6}}}$

Step 4.5.4.2

Rewrite the expression.

$\frac{{\sqrt[6]{2 s}}^{5}}{{(2 s)}^{1}}$

Step 4.5.5

Simplify.

$\frac{{\sqrt[6]{2 s}}^{5}}{2 s}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite ${\sqrt[6]{2 s}}^{5}$ as $\sqrt[6]{{(2 s)}^{5}}$ .

$\frac{\sqrt[6]{{(2 s)}^{5}}}{2 s}$

Step 5.2

Apply the product rule to $2 s$ .

$\frac{\sqrt[6]{2^{5} s^{5}}}{2 s}$

Step 5.3

Raise $2$ to the power of $5$ .

$\frac{\sqrt[6]{32 s^{5}}}{2 s}$