# How do you simplify ³sqrt(24w^2) divided by ³sqrt(3w^4)?

Mar 24, 2015

Remember that if you have roots with the same exponent their arguments can be divided under a root with that exponent.
That is
$\frac{\sqrt[a]{b}}{\sqrt[a]{c}} = \sqrt[a]{\frac{b}{c}}$

For this particular example
$\frac{\sqrt[3]{24 {w}^{2}}}{\sqrt[3]{3 {w}^{4}}}$

$= \sqrt[3]{\frac{24 {w}^{2}}{3 {w}^{4}}}$

$= \sqrt[3]{\frac{8}{w} ^ 2}$

$= 2 \sqrt[3]{\frac{1}{w} ^ 2}$

$= \frac{2}{\sqrt[3]{{w}^{2}}}$