Chapter 6.2, Problem 13WE

To determine

To calculate: The simplified form of the expression $\frac{4w}{v}\cdot \frac{v^3}{2w^2}$.

Answer to Problem 13WE

The simplified form of the expression $\frac{4w}{v}\cdot \frac{v^3}{2w^2}$ is $\frac{2v^2}{w}$.

Explanation of Solution

Given information:

The expression $\frac{4w}{v}\cdot \frac{v^3}{2w^2}$.

Formula used:

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

Calculation:

Consider the expression $\frac{4w}{v}\cdot \frac{v^3}{2w^2}$.

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,

  $\begin{array}{c}\frac{4w}{v}\cdot \frac{v^3}{2w^2}=\frac{4w\times v^3}{v\times 2w^2}\\ =\frac{4w{v}^3}{2v{w}^2}\\ =\frac{2v^2}{w}\end{array}$

Thus, the simplified form of the expression $\frac{4w}{v}\cdot \frac{v^3}{2w^2}$ is $\frac{2v^2}{w}$.