# How do you write (9y^6) ^(3/2) as a radical form?

Aug 2, 2016

${\left(9 {y}^{6}\right)}^{\frac{3}{2}}$ can be written as ${\sqrt{\left(9 {y}^{6}\right)}}^{3}$
It simplifies to $27 {y}^{9}$

#### Explanation:

One of the laws of indices states that ${x}^{\frac{p}{q}} = {\sqrt[q]{x}}^{p}$

(The denominator or the index is the root and the numerator is the power)

${\left(9 {y}^{6}\right)}^{\frac{3}{2}}$ can be written as ${\sqrt{\left(9 {y}^{6}\right)}}^{3}$

This can be simplified:
$= {\left(3 {y}^{3}\right)}^{3}$

=$27 {y}^{9}$