Chapter P.1, Problem 47E

Solution

To simplify the expression $\frac{x^4{y}^3}{x^2{y}^5}$ .

  $\frac{x^2}{y^2}$

Given:

The expression, $\frac{x^4{y}^3}{x^2{y}^5}$ .

Concept Used:

Exponent Properties:

• Product property: $a^m\cdot a^n=a^{m+n}$
• Quotient property: $\frac{a^m}{a^n}=a^{m-n}$
• Power of a power property: ${\left(a^m\right)}^n=a^{m\cdot n}$
• Negative exponent property: $a^{-n}=\frac{1}{a^n}$

Calculation:

In order to solve the given expression $\frac{x^4{y}^3}{x^2{y}^5}$ , use the exponent properties and simplify further as shown below,

  $\begin{array}{c}\frac{x^4{y}^3}{x^2{y}^5}=\frac{x^4}{x^2}\cdot \frac{y^3}{y^5}\\ =x^{4-2}\cdot y^{3-5}\\ =x^2\cdot y^{-2}\\ =x^2\cdot \frac{1}{y^2}\\ =\frac{x^2}{y^2}\end{array}$

Therefore, the simplified expression is $\frac{x^2}{y^2}$ .