Chapter 13.2, Problem 7AR

To determine

To simplify ${\left(\frac{5}{3}\right)}^{-3}$.

Answer to Problem 7AR

The required solution is ${\left(\frac{5}{3}\right)}^{-3}=\frac{1}{125/27}$ .

Explanation of Solution

Given information: The number is ${\left(\frac{5}{3}\right)}^{-3}$ .

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.

  $\begin{array}{l}{\left(\frac{5}{3}\right)}^{-3}\\ =\frac{1}{{\left(\frac{5}{3}\right)}^3}\\ =\frac{1}{\frac{125}{27}}\end{array}$

Hence, the required solution is ${\left(\frac{5}{3}\right)}^{-3}=\frac{1}{125/27}$ .