Chapter 16.5, Problem 7MRE

To determine

To simplify: the given expression.

Answer to Problem 7MRE

The simplified form of the expression is $-36p^3{q}^6$ .

Explanation of Solution

Given information:

Given expression,

  $\left(-9p{r}^4{q}^3\right)\cdot \left(4p^2{r}^{-4}{q}^3\right)$

Calculation:

Consider the given expression:

  $\left(-9p{r}^4{q}^3\right)\cdot \left(4p^2{r}^{-4}{q}^3\right)$

Now, simplify the expression as shown,

  $\begin{array}{c}\left(-9p{r}^4{q}^3\right)\cdot \left(4p^2{r}^{-4}{q}^3\right)=\left(-9\right)4p\cdot p^2{r}^4\cdot r^{-4}{q}^3\cdot q^3\\ =-36p^{1+2}{r}^{4-4}{q}^{3+3}\left[a^m\cdot a^n=a^{m+n}\right]\\ =-36p^3{r}^0{q}^6\\ =-36p^3{q}^6\end{array}$

Hence, the simplified form of the expressionis $-36p^3{q}^6$ .