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

Mar 29, 2017

${\left(\frac{2}{3}\right)}^{-} 2 = \frac{9}{4} = 2 \frac{1}{4}$

#### Explanation:

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

is a fraction with an exponent that would normally require multiplication of itself by the number of times indicated by the exponent.

In this case the exponent is negative, which must be dealt with first. A negative exponent requires that the fraction be inverted:

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

Then: ${\left(\frac{3}{2}\right)}^{2} = \left(\frac{3}{2}\right) \left(\frac{3}{2}\right) = \left(\frac{9}{4}\right) = 2 \frac{1}{4}$