Question 448057
When you talk about inversion or inverting, there are 2 basic kinds



1) Additive Inverse: Take any number and change the sign. For example, inverting 2 gives us -2. Inverting -10 gives us 10.



2) Multiplicative Inverse: Take any number and reciprocate it. If this is a whole number, divide by 1 and then flip the fraction. Ex: Invert 2 to get {{{1/2}}} (note: {{{2=2/1}}}). Ex: Invert {{{1/3}}} to get {{{3/1=3}}}



So the inverting you're talking about is the multiplicative kind. Why? Because exponents are a condensed way of writing repeated multiplication. For example {{{3^3=3*3*3}}} and {{{3^4=3*3*3*3}}}


Divide {{{3^3}}} by {{{3^4}}} to get {{{(3^3)/(3^4)=(3*3*3)/(3*3*3*3)=1/3}}}



Also note that {{{(3^3)/(3^4)=3^(3-4)=3^(-1)}}}. So {{{3^(-1)=1/3}}}



Another way to look at it: When you go from {{{3^3}}} to {{{3^4}}}, you're multiplying by 3. But to go backwards, you do the opposite of multiplication and you divide by 3, or you multiply by the multiplicative inverse of 3.