Chapter 7, Problem 13MS

To determine

To Solve: Simplify.

Answer to Problem 13MS

The simplified form of expression $\left(4m^{2}np\right)\left(-\frac{1}{4}{m}^{3}n{p}^2\right)$ is $-m^5{n}^2{p}^3$ .

Explanation of Solution

Given information:

The expression $\left(4m^{2}np\right)\left(-\frac{1}{4}{m}^{3}n{p}^2\right)$ .

Formula used:

  $a^m\cdot a^n=a^{m+n}$

Calculation:

  $\left(4m^{2}np\right)\left(-\frac{1}{4}{m}^{3}n{p}^2\right)$

Conducting the operations on like terms of $m,n,p$ constant,

  $=\left(4\cdot -\frac{1}{4}\right)\left(m^2\cdot m^3\right)\left(n\cdot n\right)\left(p\cdot p^2\right)$

Recall the property of exponents $a^m\cdot a^n=a^{m+n}$ .

  $\begin{array}{l}=\left(4\cdot -\frac{1}{4}\right)\left(m^2\cdot m^3\right)\left(n\cdot n\right)\left(p\cdot p^2\right)\\ =-1\cdot m^{2+3}\cdot n^{1+1}\cdot p^{1+1}\\ =-m^5{n}^2{p}^3\end{array}$

The simplified form of expression $\left(4m^{2}np\right)\left(-\frac{1}{4}{m}^{3}n{p}^2\right)$ is $-m^5{n}^2{p}^3$ .