Question 1198534
<font color=black size=3>
Recall that {{{a^b*a^c = a^(b+c)}}}
We add the exponents b and c. The base must stay the same the entire time.


Example:
{{{2^3*2^4 = 2^(3+4) = 2^7}}}


Also, recall that raising any nonzero value to the zeroth power gets us 1.
{{{x^0 = 1}}} where x is nonzero
Example
{{{6^0 = 1}}}


What we can do is the following steps
{{{6^0 = 6^(3-3)}}}


{{{6^0 = 6^(3+(-3))}}}


{{{6^0 = 6^(3)*6^(-3))}}} use the a^b*a^c = a^(b+c) rule mentioned earlier.


Then replace the 6^0 with 1 and isolate the {{{6^(-3)}}} term
{{{1 = 6^(3)*6^(-3))}}}


{{{6^(-3) = 1/(6^3)}}}


------------------------------------------------


In general:
{{{a^(b-b) = a^0}}}


{{{a^(b+(-b)) = 1}}}


{{{a^b*a^(-b) = 1}}}


{{{a^(-b) = 1/(a^b)}}}
where {{{a <> 0}}}
</font>