Chapter 7, Problem 7CT

To determine

To Perform: The indicated operation.

Answer to Problem 7CT

  $\frac{1}{4y^3}$

Explanation of Solution

Given: $\frac{3x^{2}y}{4x^3{y}^5}÷\frac{6y^2}{2x{y}^3}$

Properties used:

  $\begin{array}{l}{x}^a\times x^b=x^{a+b}\\ \frac{x^a}{x^b}=x^{a-b}\end{array}$

Given: $\frac{3x^{2}y}{4x^3{y}^5}÷\frac{6y^2}{2x{y}^3}$

Solving

  $\begin{array}{l}=\frac{3x^{2}y}{4x^3{y}^5}÷\frac{6y^2}{2x{y}^3}\\ =\frac{3x^{2}y}{4x^3{y}^5}\times \frac{2x{y}^3}{6y^2}\\ =\frac{6x^3{y}^4}{24x^3{y}^7}\\ =\frac{1}{4y^3}\end{array}$

Hence, $\frac{1}{4y^3}$