How do you simplify $\frac{\sqrt{7}}{\sqrt[5]{7}}$ $sqrt7/root5(7)$ ?

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How do you simplify $\frac{\sqrt{7}}{\sqrt[5]{7}}$ $sqrt7/root5(7)$ ?

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Answer 1 · 2016-07-28T19:35:35

$= \sqrt[10]{7^{3}}$ $=root10(7^3$

Explanation:

$\frac{\sqrt{7}}{\sqrt[5]{7}}$ $sqrt7/root5(7)$
$= \frac{7^{\frac{1}{2}}}{7^{\frac{1}{5}}}$ $=7^(1/2)/(7^(1/5))$
$= 7^{(\frac{1}{2} - \frac{1}{5})}$ $=7^((1/2-1/5))$
$= 7^{\frac{5 - 2}{10}}$ $=7^((5-2)/10$
$= 7^{\frac{3}{10}}$ $=7^(3/10)$
$= \sqrt[10]{7^{3}}$ $=root10(7^3$

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