How do you simplify $5 \sqrt{\frac{1}{3125}}$ $5 sqrt (1/3125)$ ?

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Answer 1 · 2016-07-07T14:15:12

$\frac{1}{5}$ $1/5$

$\sqrt[x]{\frac{a}{b}} = \frac{\sqrt[x]{a}}{\sqrt[x]{b}}$ $root(x)(a/b) = (rootxa)/(rootxb)$

$\sqrt[5]{\frac{1}{3125}} = \frac{\sqrt[5]{1}}{\sqrt[5]{3125}}$ $root5 (1/3125) = root5 1/root5 3125$

$= \frac{1}{5}$ $= 1/5$

Check work:

$\frac{1 \cdot 1 \cdot 1 \cdot 1 \cdot 1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5}$ $(1*1*1*1*1)/(5*5*5*5*5)$

$\frac{1}{3125}$ $1/(3125)$

How do you simplify 5√131255 sqrt (1/3125)?