# How do you simplify 13^4 / sqrt(13^10)?

##### 2 Answers
Jun 13, 2016

${13}^{4} / \left(\sqrt{{13}^{10}}\right) = \frac{1}{13}$

#### Explanation:

13^4/(sqrt(13^10)

= ${13}^{4} / {\left({13}^{10}\right)}^{\frac{1}{2}}$

= ${13}^{4} / \left({13}^{\left(10 \times \frac{1}{2}\right)}\right)$

= ${13}^{4} / {13}^{5}$

= $\frac{13 \times 13 \times 13 \times 13}{13 \times 13 \times 13 \times 13 \times 13}$

= $\frac{1}{13}$

Jun 14, 2016

Demonstration of a very slightly different method.

$\frac{1}{13}$

#### Explanation:

Another way of writing $\sqrt{{13}^{10}} \text{ }$ is $\text{ } {13}^{\frac{10}{2}}$

But we have $\frac{1}{\sqrt{{13}^{10}}} \text{ }$ which is the same as ${13}^{- \frac{10}{2}}$

So $\text{ } {13}^{4} / \sqrt{{13}^{10}} = {13}^{4} \times {10}^{- \frac{10}{2}}$

But $\frac{10}{2} = 5$ giving

${13}^{4} \times {13}^{- 5}$

${13}^{4 - 5} = {13}^{- 1} = \frac{1}{13}$