# How do you solve x^(3/2) = 27?

Jun 29, 2016

$x = 9.$

#### Explanation:

Given Eqn. : ${x}^{\frac{3}{2}} = 27.$
$\therefore {\left\{{x}^{\frac{3}{2}}\right\}}^{2} = {27}^{2.}$
$\therefore {x}^{\frac{3}{2} \cdot 2} = {\left({3}^{3}\right)}^{2.}$
$\therefore {x}^{3} = {3}^{3 \cdot 2} = {3}^{6} = {\left({3}^{2}\right)}^{3.}$
As powers are same, so must be the bases, so, $x = {3}^{2} = 9.$

It can be easily verified that the root found satisfies the given eqn. Hence, the Soln. is $x = 9.$