Chapter 8.1, Problem 10CYU

To determine

Simplify the given expression.

Answer to Problem 10CYU

The required simplified expression is $\frac{a{b}^2}{y^3}$ .

Explanation of Solution

Given information: Given the expression is $\frac{\frac{a^3{b}^3}{x{y}^4}}{\frac{a^{2}b}{x^{2}y}}$ .

Calculation:

Given the expression:

  $\begin{array}{l}\frac{\frac{a^3{b}^3}{x{y}^4}}{\frac{a^{2}b}{x^{2}y}}=\frac{a^3{b}^3}{x{y}^4}\cdot \frac{x^{2}y}{a^{2}b}\\ =\frac{a\cdot a\cdot a\cdot b\cdot b\cdot b\cdot x\cdot x\cdot y}{x\cdot y\cdot y\cdot y\cdot y\cdot a\cdot a\cdot b}\text{ multifly across the top and bottam}\\ =\frac{a{b}^2}{y^3}\text{ cancel out like terms}\end{array}$

Thus, the required simplified expression is $\frac{a{b}^2}{y^3}$