<PRE><B>Question 1198534</B>

Concerning negative exponents, why is the reciprocal of a fraction a positive one in the numerator? Instead of a negative one.
e.g.
 6^-3 = 1 / 6^3 vs. 6^-3 = -1 / 6^3 
&lt;pre&gt;&lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;6&lt;sup&gt;-3&lt;/sup&gt; = {{{1/6^3}}} vs. 6&lt;sup&gt;-3&lt;/sup&gt; = {{{(cross(-1))1/6^3}}}&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;
&lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;6&lt;sup&gt;-3&lt;/sup&gt; = {{{(6/1)^(-3)}}} = {{{(1/6)^3}}}&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;.
As seen above, the 6 in the numerator and the 1 in the denominator are BOTH positive. They can&#39;t,
all of a sudden, become negative. Then, they TRADE PLACES, but DEFINITELY remain positive.
They can&#39;t, all of a sudden, become negative.

Now, if we had: &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;(- 6)&lt;sup&gt;-3&lt;/sup&gt;&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, then that&#39;s the same as: {{{(- 6/1)^(- 3)}}}, which would then be:{{{matrix(1,3, ((- 6)/1)^(- 3), or, (6/(- 1))^(- 3))}}}.

                         {{{(- 6/1)^(- 3)}}} then becomes: {{{(- 1/6)^3}}}, which can also be written as: {{{matrix(1,3, ((- 1)/6)^3, or, (1/(- 6))^3)}}}

As seen above, either the numerator, 1, or the denominator, 6, can be negative, as a result of the - 6 that was given!&lt;/pre&gt;</PRE>