Chapter 12, Problem 15CLR

To determine

To Evaluate: The simplified value of the expression $\frac{-72w{x}^4{y}^{5}z}{-96x^3{y}^{7}z}$ .

Answer to Problem 15CLR

The value of the expression $\frac{-72w{x}^4{y}^{5}z}{-96x^3{y}^{7}z}$ is $\frac{3}{4y^2}wx$ .

Explanation of Solution

Given information:

The expression is $\frac{-72w{x}^4{y}^{5}z}{-96x^3{y}^{7}z}$ .

Formula used:

When an algebraic term is divided by another algebraic term power of same variable subtracted and the numerical coefficients divided.

Example-:

  $\frac{7a^8}{14a^2}=\frac{7}{14}{a}^{8-2}$

Calculation:

Consider the expression is $\frac{-72w{x}^4{y}^{5}z}{-96x^3{y}^{7}z}$ .

Recall that when an algebraic term is divided by another algebraic term power of same variable subtracted and the numerical coefficients divided.

Apply it,

  $\begin{array}{c}\frac{-72w{x}^4{y}^{5}z}{-96x^3{y}^{7}z}=\frac{-72}{-96}{w}^{1-0}{x}^{4-3}{y}^{5-7}{z}^{1-1}\\ =\frac{3}{4}wx{y}^{-2}{z}^0\\ =\frac{3}{4}wx\frac{1}{y^2}\times 1\\ =\frac{3}{4y^2}wx\end{array}$

Thus, the value of the expression $\frac{-72w{x}^4{y}^{5}z}{-96x^3{y}^{7}z}$ is $\frac{3}{4y^2}wx$ .