Chapter 4.2, Problem 24WE

To determine

Simplify the expression $y^{p+2}\cdot y^p\cdot y^{p-2}$ if the exponents of variables represent positive integers.

Answer to Problem 24WE

The simplified value of expression is $y^{3p}$ .

Explanation of Solution

Given information: The given expression is $y^{p+2}\cdot y^p\cdot y^{p-2}$ .

Calculation: Simplifying the expression $y^{p+2}\cdot y^p\cdot y^{p-2}$ ,

  $\begin{array}{c}{y}^{p+2}\cdot y^p\cdot y^{p-2}={\left(y\right)}^{\left(p+2\right)+\left(p\right)+\left(p-2\right)}\mathrm{....}\left\{{\left(x\right)}^a{\left(x\right)}^b{\left(x\right)}^c={\left(x\right)}^{a+b+c}\right\}\\ =y^{3p}\end{array}$