Chapter 8.1, Problem 4CGP

To determine

Simplify the given expression.

Answer to Problem 4CGP

The required simplified expression is $\frac{t^2}{12m^2{a}^{2}b}$

Explanation of Solution

Given information: Given the expression is $\frac{6m{t}^2}{21a^4{b}^3}÷\frac{24m^3}{7a^2{b}^2}$

Calculation:

  $\begin{array}{l}=\frac{6m{t}^2}{21a^4{b}^3}÷\frac{24m^3}{7a^2{b}^2}\\ =\frac{6m{t}^2}{21a^4{b}^3}\cdot \frac{7a^2{b}^2}{24m^3}\text{ Rewrite}\\ =\frac{3\cdot 2m{t}^2}{7\cdot 3a^4{b}^3}\cdot \frac{7a^2{b}^2}{3\cdot 2\cdot 4m^3}\text{ Rewrite}\\ =\frac{m{t}^2}{3a^4{b}^3}\cdot \frac{a^2{b}^2}{4m^3}\text{ Cancel like terms}\\ =\frac{t^2}{3a^{2}b}\cdot \frac{1}{4m^2}\text{ Cancel like terms}\\ =\frac{t^2}{12m^2{a}^{2}b}\text{ Multiply}\end{array}$

Thus, the required simplified expression is $\frac{t^2}{12m^2{a}^{2}b}$