Chapter 5.1, Problem 65HP

To determine

To proof: The property of negative exponent can we proven using the quotient of powers property.

Explanation of Solution

Given information:

The given exponent property is $\frac{1}{a^n}$ .

Calculation:

Consider the zero property power $a^0$ will always equal $1$ , so we can replace $1$ with $a^0$ .

  $\frac{a^0}{a^n}$ .

Thus, quotient of powers, subtract exponent to divide.

  $\begin{array}{l}=a^{0-n}\\ =a^{-n}\end{array}$

From the above, it is clear that the exponent power can be negative.

Hence,proved.