How do you simplify $\sqrt[3]{\frac{8}{125}}$ $root3(8/125)$ ?

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Answer 1 · 2015-09-21T14:16:51

$\frac{2}{5}$ $2/5$

You have
$\sqrt[3]{\frac{8}{125}}$ $root(3)(8/125)$

You should notice that:
$8 = 2^{3}$ $8=2^3$
and
$125 = 5^{3}$ $125=5^3$

Rewriting, you have
$\sqrt[3]{\frac{2^{3}}{5^{3}}}$ $root(3)((2^3)/(5^3))$

which becomes
$\frac{\sqrt[3]{2^{3}}}{\sqrt[3]{5^{3}}}$ $(root(3)(2^3))/(root(3)(5^3))$
$= \frac{2}{5}$ $=2/5$

How do you simplify root3(8/125)3√8125root3(8/125)?