Chapter 7.1, Problem 6STP

For Exercises $1-6,$ choose the correct letter.

What is the simplified form of ${\left(-\frac{5a}{3}\right)}^{-3}?$

F. $\frac{27}{125a^3}$

G. $-\frac{27}{125a^3}$

H. $\frac{125a^3}{27}$

I $-\frac{125a^3}{27}$

To determine

To simplify the given expression.

Answer to Problem 6STP

  ${\left(-\frac{5a}{3}\right)}^{-3}=-\frac{27}{125a^3}$ & option G is correct.

Explanation of Solution

Given:

  ${\left(-\frac{5a}{3}\right)}^{-3}$

Concept used:

  $a^{-m}=\frac{1}{a^m},a\ne 0$

Calculation:

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

Hence option G is correct.