Chapter 12, Problem 12CLR

To determine

To Evaluate: The simplified value of the expression $\left(-\frac{1}{8}{x}^5{y}^{3}z\right)\left(-24x^{2}y\right)$ .

Answer to Problem 12CLR

The value of the expression $\left(-\frac{1}{8}{x}^5{y}^{3}z\right)\left(-24x^{2}y\right)$ is $3x^7{y}^{4}z$ .

Explanation of Solution

Given information:

The expression is $\left(-\frac{1}{8}{x}^5{y}^{3}z\right)\left(-24x^{2}y\right)$ .

Formula used:

When a algebraic term is multiply by another algebraic term power of same variable added and

the numerical coefficients multiply together.

Example-:

  $\begin{array}{c}5x^{2}y\times \left(-7x\right)=-35xy{}^{1+0}\\ =-35x^3{y}^1\end{array}$

Calculation:

Consider the expression is $\left(-\frac{1}{8}{x}^5{y}^{3}z\right)\left(-24x^{2}y\right)$ .

Recall that when a algebraic term is multiply by another algebraic term power of same variable

added and the numerical coefficients multiply together.

Apply it,

  $\begin{array}{c}\left(-\frac{1}{8}{x}^5{y}^{3}z\right)\left(-24x^{2}y\right)=\left(-\frac{1}{8}\right)\left(-24\right)x^{5+2}{y}^{3+1}{z}^{1+0}\\ =3x^7{y}^{4}z\end{array}$

Thus, the value of the expression $\left(-\frac{1}{8}{x}^5{y}^{3}z\right)\left(-24x^{2}y\right)$ is $3x^7{y}^{4}z$ .