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

Oct 28, 2015

${\left(\frac{2}{3}\right)}^{- 3} = \frac{27}{8} = 3 \frac{3}{8}$

#### Explanation:

In general ${a}^{- b} = \frac{1}{{A}^{b}}$

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

$\textcolor{w h i t e}{\text{XXXXXXXX}} = \frac{1}{\frac{{2}^{3}}{{3}^{3}}}$

$\textcolor{w h i t e}{\text{XXXXXXXX}} = \frac{{3}^{3}}{{2}^{3}}$

$\textcolor{w h i t e}{\text{XXXXXXXX}} = \frac{27}{8}$

Oct 28, 2015

$\frac{27}{8}$

#### Explanation:

A negative power is the same thing as the positive power of the inverse number.

So, first of all, ${\left(\frac{2}{3}\right)}^{- 3}$ is the same thing as ${\left(\frac{3}{2}\right)}^{3}$.

Now we have to compute the power of a fraction, which is very simple, because it is the power of the numerator divided by the power of the denominator, so

${\left(\frac{3}{2}\right)}^{3} = {3}^{3} / {2}^{3} = \frac{27}{8}$