Chapter 5.1, Problem 7WE

To determine

To find: Simplify the given expression.

Answer to Problem 7WE

  ${\left(\frac{3r}{s^2}\right)}^3=\frac{27r^3}{s^6}$

Explanation of Solution

Given information:

  ${\left(\frac{3r}{s^2}\right)}^3$

Concept:

Using law of exponents

  ${\left(a^m\right)}^n=a^{mn}$

Where $a$ be any value.

  ${\left(\frac{3r}{s^2}\right)}^3$

  $\begin{array}{l}\Rightarrow {\left(\frac{3r}{s^2}\right)}^3=\frac{{\left(3r\right)}^3}{{\left(s^2\right)}^3}\\ \Rightarrow {\left(\frac{3r}{s^2}\right)}^3=\frac{27r^3}{s^{2\times 3}}\\ \Rightarrow {\left(\frac{3r}{s^2}\right)}^3=\frac{27r^3}{s^6}\end{array}$

Therefore,

  ${\left(\frac{3r}{s^2}\right)}^3=\frac{27r^3}{s^6}$