Algebra Examples

$\frac{r}{\sqrt{6 r^{6}}}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

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

$\frac{r}{\sqrt{6 {(r^{3})}^{2}}}$

Step 1.1.2

Reorder $6$ and ${(r^{3})}^{2}$ .

$\frac{r}{\sqrt{{(r^{3})}^{2} \cdot 6}}$

Step 1.2

Pull terms out from under the radical.

$\frac{r}{r^{3} \sqrt{6}}$

Step 2

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

Tap for more steps...

Step 2.1

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

$\frac{r^{1}}{r^{3} \sqrt{6}}$

Step 2.2

Factor $r$ out of $r^{1}$ .

$\frac{r \cdot 1}{r^{3} \sqrt{6}}$

Step 2.3

Cancel the common factors.

Tap for more steps...

Step 2.3.1

Factor $r$ out of $r^{3} \sqrt{6}$ .

$\frac{r \cdot 1}{r (r^{2} \sqrt{6})}$

Step 2.3.2

Cancel the common factor.

$\frac{r \cdot 1}{r (r^{2} \sqrt{6})}$

Step 2.3.3

Rewrite the expression.

$\frac{1}{r^{2} \sqrt{6}}$

Step 3

Multiply $\frac{1}{r^{2} \sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{1}{r^{2} \sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$

Step 4

Combine and simplify the denominator.

Tap for more steps...

Step 4.1

Multiply $\frac{1}{r^{2} \sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{\sqrt{6}}{r^{2} \sqrt{6} \sqrt{6}}$

Step 4.2

Move $\sqrt{6}$ .

$\frac{\sqrt{6}}{r^{2} (\sqrt{6} \sqrt{6})}$

Step 4.3

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{\sqrt{6}}{r^{2} ({\sqrt{6}}^{1} \sqrt{6})}$

Step 4.4

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{\sqrt{6}}{r^{2} ({\sqrt{6}}^{1} {\sqrt{6}}^{1})}$

Step 4.5

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

$\frac{\sqrt{6}}{r^{2} {\sqrt{6}}^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$\frac{\sqrt{6}}{r^{2} {\sqrt{6}}^{2}}$

Step 4.7

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Tap for more steps...

Step 4.7.1

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

$\frac{\sqrt{6}}{r^{2} {(6^{\frac{1}{2}})}^{2}}$

Step 4.7.2

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

$\frac{\sqrt{6}}{r^{2} \cdot 6^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

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

$\frac{\sqrt{6}}{r^{2} \cdot 6^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.7.4.1

Cancel the common factor.

$\frac{\sqrt{6}}{r^{2} \cdot 6^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{\sqrt{6}}{r^{2} \cdot 6^{1}}$

Step 4.7.5

Evaluate the exponent.

$\frac{\sqrt{6}}{r^{2} \cdot 6}$

Step 5

Move $6$ to the left of $r^{2}$ .

$\frac{\sqrt{6}}{6 r^{2}}$