Chapter 4.6, Problem 42E

To determine

To prove when $a=0$ , the rule $a^{-n}=\frac{1}{a^n}$ does not apply.

Answer to Problem 42E

Rule $a^{-n}=\frac{1}{a^n}$ does not apply when $a=0$

Explanation of Solution

Given information: $a^{-n}=\frac{1}{a^n}$ and $a=0$

The rule stated does not hold true when $a=0$ . This is because, if any fraction has a denominator as zero, the fraction becomes undefined and tends towards infinity.

Here replace the value of a in $\frac{1}{a^n}$ with zero, $\frac{1}{0}=\infty$