Chapter 6.2, Problem 16WE

To determine

To calculate: The simplified form of the expression $\frac{2r{s}^2}{3t}\cdot \frac{9t^2}{4rs}$.

Answer to Problem 16WE

The simplified form of the expression $\frac{2r{s}^2}{3t}\cdot \frac{9t^2}{4rs}$ is $\frac{3st}{2}$.

Explanation of Solution

Given information:

The expression $\frac{2r{s}^2}{3t}\cdot \frac{9t^2}{4rs}$.

Formula used:

Fractions are multiplied as $\frac{a}{b}\cdot \frac{c}{d}=\frac{ab}{cd}$.

Calculation:

Consider the expression $\frac{2r{s}^2}{3t}\cdot \frac{9t^2}{4rs}$.

Recall that fractions are multiplied as $\frac{a}{b}\cdot \frac{c}{d}=\frac{ab}{cd}$ and law of exponent $\frac{a^m}{a^n}=a^{m-n}$.

Apply it,

  $\begin{array}{c}\frac{2r{s}^2}{3t}\cdot \frac{9t^2}{4rs}=\frac{2r{s}^2\times 9t^2}{3t\times 4rs}\\ =\frac{3r{s}^2{t}^2}{2rst}\\ =\frac{3st}{2}\end{array}$

Thus, the simplified form of the expression $\frac{2r{s}^2}{3t}\cdot \frac{9t^2}{4rs}$ is $\frac{3st}{2}$.