# Question #81fe9

Dec 30, 2016

(see below)

#### Explanation:

Consider the relationship between decreasing powers of any number.

If we let $n$ be such a number then we see that (for example):
$\textcolor{w h i t e}{\text{XXX}} {n}^{4} = {n}^{5} \div n$

$\textcolor{w h i t e}{\text{XXX}} {n}^{3} = {n}^{4} \div n$

$\textcolor{w h i t e}{\text{XXX}} {n}^{2} = {n}^{3} \div n$

$\textcolor{w h i t e}{\text{XXX}} {n}^{1} = {n}^{2} \div n$

if we continue...
$\textcolor{w h i t e}{\text{XXX}} {n}^{0} = {n}^{1} \div n$ (n.b. this is just $n \div n = 1$)
and
$\textcolor{w h i t e}{\text{XXX}} {n}^{- 1} = {n}^{0} \div n$ (that is $1 \div n = \frac{1}{n}$; the reciprocal of $n$)