Chapter 7.5, Problem 58CCR

To determine

Find the quotient of $\frac{a^3}{a^{-3}}$

Answer to Problem 58CCR

  $\frac{a^3}{a^{-3}}=a^6$

Explanation of Solution

Given:

Find the quotient of $\frac{a^3}{a^{-3}}$

Concept Used:

  $\text{Negative}\text{exponent}\text{rule}:\frac{1}{a^{-m}}=a^m$

  $\text{Product}\text{rule}=a^m·a^n=a^{m+n}$

Calculation:

Find the quotient of $\frac{a^3}{a^{-3}}$

  $\begin{array}{l}\frac{a^3}{a^{-3}}=a^3·a^3[\frac{1}{a^{-m}}=a^m]\\ a^3·a^3=a^{3+3}=a^6[a^m·a^n=a^{m+n}]\\ \frac{a^3}{a^{-3}}=a^6\end{array}$

Thus, $\frac{a^3}{a^{-3}}=a^6$