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

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Answer 1 · 2016-06-13T04:36:35

$13^4/(sqrt(13^10))=1/13$

$13^4/(sqrt(13^10)$

= $13^4/(13^10)^(1/2)$

= $13^4/(13^((10xx1/2)))$

= $13^4/13^5$

= $(13xx13xx13xx13)/(13xx13xx13xx13xx13)$

= $1/13$

Answer 2 · 2016-06-14T11:22:14

Demonstration of a very slightly different method.

$1/13$

Another way of writing $sqrt(13^10)" "$ is $" "13^(10/2)$

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

So $" "13^4/sqrt(13^10) = 13^4xx10^(-10/2)$

But $10/2=5$ giving

$13^4xx13^(-5)$

$13^(4-5)= 13^(-1) = 1/13$

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