Chapter 4.3, Problem 61HP

To determine

To find: the two algebraic expression.

Answer to Problem 61HP

The algebraic expression are $x^8÷x^3$ and $x^3÷x^{-2}$ whose quotient is $x^5$ .

Explanation of Solution

Given information:

Quotient is $x^5$ .

Calculation : let expression $x^8÷x^3$ ,

  $\begin{array}{l}{x}^8÷x^3=x^{8-3}\text{ [}{a}^m÷a^n=a^{m-n}]\\ x^8÷x^3=x^5\text{ [simplify the exponents]}\end{array}$

Let expression is $x^3÷x^{-2}$ ,

  $\begin{array}{l}{x}^3÷x^{-2}=x^{3-\left(-2\right)}\text{ [}{a}^m÷a^n=a^{m-n}]\\ x^3÷x^{-2}=x^5\text{ [simplify the exponents]}\end{array}$

Thus the expression are $x^8÷x^3$ and $x^3÷x^{-2}$