# How do you simplify (100/9)^(3/2)?

Apr 29, 2016

$\frac{1000}{27}$

#### Explanation:

Power of $\frac{2}{3}$ is first to take the square root of $\frac{100}{9}$ which is $\frac{10}{3}$, then cube that answer, which is $\frac{1000}{27}$.

Apr 29, 2016

$\frac{1000}{27}$
${\left(\frac{100}{9}\right)}^{\frac{3}{2}} = {\left({\left(\frac{10}{3}\right)}^{2}\right)}^{\frac{3}{2}} = {\left(\frac{10}{3}\right)}^{2 \times \left(\frac{3}{2}\right)} = {\left(\frac{10}{3}\right)}^{3} = \frac{1000}{27}$