Chapter 10.1, Problem 30E

To determine

To calculate:

Product of the given expression.

Answer to Problem 30E

The product of $\frac{4x^{9}y}{3x^3}.\frac{2xy}{8y^2}$ is $\frac{x^7}{3}$ .

Explanation of Solution

Given information:

Expression:

  $\frac{4x^{9}y}{3x^3}.\frac{2xy}{8y^2}$

Calculation:

Product of the given expression is calculated as,

  $\begin{array}{l}=\frac{4x^{9}y}{3x^3}.\frac{2xy}{8y^2}\\ =\frac{3x.2x^3}{y^3}\end{array}$

Lets take first term,

  $\begin{array}{l}\frac{4x^{9}y}{3x^3}\\ =\frac{4x^{6}y}{3}\end{array}$

Take another term for simplification,

  $\begin{array}{l}\frac{2xy}{8y^2}\\ =\frac{2x}{8y}\\ =\frac{x}{4y}\end{array}$

Product of two terms,

  $\begin{array}{l}=\frac{x}{4y}.\frac{4x^{6}y}{3}\\ =\frac{x.4x^{6}y}{4y.3}\\ =\frac{4x^{6}yx}{3.4y}\\ =\frac{x^{6}yx}{3y}\\ =\frac{x^{6}x}{3}\\ =\frac{x^7}{3}\end{array}$

Hence, the product of $\frac{4x^{9}y}{3x^3}.\frac{2xy}{8y^2}$ is $\frac{x^7}{3}$ .