How do you simplify $\frac{13^{4}}{\sqrt{13^{10}}}$ $13^4 / sqrt(13^10)$ ?

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Answer 1 · 2016-06-13T04:36:35

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

$\frac{13^{4}}{\sqrt{13^{10}}}$ $13^4/(sqrt(13^10)$

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

= $\frac{13^{4}}{13^{(10 \times \frac{1}{2})}}$ $13^4/(13^((10xx1/2)))$

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

= $\frac{13 \times 13 \times 13 \times 13}{13 \times 13 \times 13 \times 13 \times 13}$ $(13xx13xx13xx13)/(13xx13xx13xx13xx13)$

= $\frac{1}{13}$ $1/13$

Answer 2 · 2016-06-14T11:22:14

Demonstration of a very slightly different method.

$\frac{1}{13}$ $1/13$

Another way of writing $\sqrt{13^{10}}$ $sqrt(13^10)" "$ is $13^{\frac{10}{2}}$ $" "13^(10/2)$

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

So $\frac{13^{4}}{\sqrt{13^{10}}} = 13^{4} \times 10^{- \frac{10}{2}}$ $" "13^4/sqrt(13^10) = 13^4xx10^(-10/2)$

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

$13^{4} \times 13^{- 5}$ $13^4xx13^(-5)$

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

How do you simplify 134√131013^4 / sqrt(13^10)?