How do you write (16/25)^(3/2) as radical form?

Jan 7, 2016

${\left(\frac{16}{25}\right)}^{\frac{3}{2}} = \pm {\left(\frac{\sqrt{16}}{\sqrt{25}}\right)}^{3}$

Explanation:

${b}^{\frac{1}{2}} = \sqrt{b} \textcolor{w h i t e}{\text{XXX}}$ and $\textcolor{w h i t e}{\text{XXX}} {b}^{\frac{3}{2}} = {\left({b}^{\frac{1}{2}}\right)}^{3}$

Note
$\textcolor{w h i t e}{\text{XXX}} {\left(\pm \frac{\sqrt{16}}{\sqrt{25}}\right)}^{3}$ could be simplified as $\pm \frac{{4}^{3}}{{5}^{3}} = \pm \frac{64}{125}$

but then it would no longer be in "radical form"