Chapter 4.2, Problem 8WE

To determine

Simplify the expression $\left(r^{2}s\right)\left(-3r{s}^3\right)\left(2rs\right)$ if the exponents of variables represent positive integers.

Answer to Problem 8WE

The simplified value of expression is $-6r^4{s}^5$ .

Explanation of Solution

Given information: The given expression is $\left(r^{2}s\right)\left(-3r{s}^3\right)\left(2rs\right)$ .

Calculation: Simplifying the expression $\left(r^{2}s\right)\left(-3r{s}^3\right)\left(2rs\right)$ ,

  $\begin{array}{c}\left(r^{2}s\right)\left(-3r{s}^3\right)\left(2rs\right)=\left(-6\right)\left(r^{2}s\right)\left(r{s}^3\right)\left(rs\right)\\ =\left(-6\right)\left(r^{2+1+1}\right)\left(s^{1+3+1}\right)\mathrm{....}\left\{{\left(x\right)}^m{\left(x\right)}^n={\left(x\right)}^{m+n}\right\}\\ =-6r^4{s}^5\end{array}$