Chapter 13.2, Problem 6AR

To determine

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

Answer to Problem 6AR

The required solution is ${\left(\frac{2}{3}\right)}^{-2}=\frac{1}{4/9}$ .

Explanation of Solution

Given information: The number is ${\left(\frac{2}{3}\right)}^{-2}$ .

Calculation: The required solution is obtained as,

When there is a negative exponent, just put the whole thing under 1 and get rid of the negative.

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

Hence, the required solution is ${\left(\frac{2}{3}\right)}^{-2}=\frac{1}{4/9}$ .