Chapter 4.2, Problem 25WE

To determine

Simplify the expression $r^{h-2}{\left(r^{h+1}\right)}^2$ if the exponents of variables represent positive integers.

Answer to Problem 25WE

The simplified value of expression is $r^{3h}$ .

Explanation of Solution

Given information: The given expression is $r^{h-2}{\left(r^{h+1}\right)}^2$ .

Calculation: Simplifying the expression $r^{h-2}{\left(r^{h+1}\right)}^2$ ,

  $\begin{array}{c}{r}^{h-2}{\left(r^{h+1}\right)}^2={\left(r\right)}^{h-2}{\left(r\right)}^{2\left(h+1\right)}\mathrm{....}\left\{{\left(x^a\right)}^b={\left(x\right)}^{ab}\right\}\\ ={\left(r\right)}^{h-2}{\left(r\right)}^{2h+2}\\ ={\left(r\right)}^{\left(h-2\right)+\left(2h+2\right)}\\ =r^{3h}\end{array}$