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

Sep 11, 2016

The result is $\frac{9}{4}$ or $2 \frac{1}{4}$

#### Explanation:

${\left(- \left(\frac{2}{3}\right)\right)}^{- 2} = {\left(- \frac{3}{2}\right)}^{2} = \frac{9}{4}$

In the calculation I used the following property of powers:

${a}^{-} b = {\left(\frac{1}{a}\right)}^{b}$

Sep 11, 2016

$\frac{9}{4}$

#### Explanation:

We have: ${\left(- \left(\frac{2}{3}\right)\right)}^{- 2}$

First, let's expand the parentheses:

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

Then, using the laws of exponents:

$= \frac{1}{{\left(- \frac{2}{3}\right)}^{2}}$

$= \frac{1}{{\left(\frac{- 2}{3}\right)}^{2}}$

$= \frac{1}{\left({\left(- 2\right)}^{2} / {\left(3\right)}^{2}\right)}$

$= \frac{1}{\left(\frac{4}{9}\right)}$

$= 1 \cdot \left(\frac{9}{4}\right)$

$= \frac{9}{4}$