Chapter 8.1, Problem 28PPS

To determine

Simplify the given expression.

Answer to Problem 28PPS

The required simplified expression is $\frac{15y^3}{2xz}$ .

Explanation of Solution

Given information: Given the expression is $\frac{9x^{2}yz}{5z^4}÷\frac{12x^4{y}^2}{50x{y}^4{z}^2}$ .

Calculation:

Given the expression:

  $\begin{array}{l}\frac{9x^{2}yz}{5z^4}÷\frac{12x^4{y}^2}{50x{y}^4{z}^2}\\ =\frac{9x^{2}yz}{5z^4}÷\frac{6x^4{y}^2}{25x{y}^4{z}^2}\text{ multiply }\\ =\frac{9x^{2}yz}{5z^4}\cdot \frac{25x{y}^4{z}^2}{6x^4{y}^2}\text{ cacel the common factor }\\ =\frac{3x^{2}yz}{z^4}\cdot \frac{5x{y}^4{z}^2}{2x^4{y}^2}\\ =\frac{15y^3}{2xz}\end{array}$

Thus, the required simplified expression is $\frac{15y^3}{2xz}$