<PRE><B>Question 69602</B>
&lt;pre&gt;&lt;font size = 5&gt;&lt;b&gt;
Write in simplest form.   

   {{{(5r^3st^2)/(-10r^6s^3t)}}}

I have come up with

   {{{t/(-2r^-3s^-2)}}}

Can someone look this over and let me know if 
I am on the right track???

--------------------------------------------------------

You should get POSITIVE exponents in the bottom where
you have NEGATIVE exponents.  How did you manage to
get them NEGATIVE?? 

Let&#39;s go through it the most basic way so you 
will see:

  5r&lt;sup&gt;3&lt;/sup&gt;st&lt;sup&gt;2&lt;/sup&gt;
----------
 -10r&lt;sup&gt;6&lt;/sup&gt;s&lt;sup&gt;3&lt;/sup&gt;t

Break everything down into prime factors

      5·r·r·r·s·t·t
--------------------------
 -2·5·r·r·r·r·r·r·s·s·s·t

Cancel the 5&#39;s

      1
      &lt;s&gt;5&lt;/s&gt;·r·r·r·s·t·t
--------------------------
 -2·&lt;s&gt;5&lt;/s&gt;·r·r·r·r·r·r·s·s·s·t
    1

Cancel the three r&#39;s in the top with three
of the r&#39;s in the bottom:
 
      1 1 1 1  
      &lt;s&gt;5&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·s·t·t
--------------------------
 -2·&lt;s&gt;5&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·r·r·r·s·s·s·t
    1 1 1 1

Cancel the s in the top with one of the s&#39;s 
in the bottom:

      1 1 1 1 1  
      &lt;s&gt;5&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;s&lt;/s&gt;·t·t
--------------------------
 -2·&lt;s&gt;5&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·r·r·r·&lt;s&gt;s&lt;/s&gt;·s·s·t
    1 1 1 1       1

Cancel the t in the bottom with one of the 
t&#39;s in the top

      1 1 1 1 1 1 
      &lt;s&gt;5&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;s&lt;/s&gt;·&lt;s&gt;t&lt;/s&gt;·t
--------------------------
 -2·&lt;s&gt;5&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·&lt;s&gt;r&lt;/s&gt;·r·r·r·&lt;s&gt;s&lt;/s&gt;·s·s·&lt;s&gt;t&lt;/s&gt;
    1 1 1 1       1     1

Erase all that canceled out and this is 
what we have left:
                  
                  t
--------------------------
 -2·        r·r·r·  s·s

Close up the gaps:

       t
---------------
 -2·r·r·r·s·s

Bring the negative sign from the bottom
and put it out front of the fraction:

        t
- -------------
   2·r·r·r·s·s

Write r&lt;sup&gt;3&lt;/sup&gt; for r·r·r and s&lt;sup&gt;2&lt;/sup&gt; for s·s

      t
- ---------
   2·r&lt;sup&gt;3&lt;/sup&gt;·s&lt;sup&gt;2&lt;/sup&gt;

We can erase the dots for multiplication:

     t
- -------
   2r&lt;sup&gt;3&lt;/sup&gt;s&lt;sup&gt;2&lt;/sup&gt;

A quicker way to do the problem is to use this rule:

If an exponential factor of the top has the same base
as an exponential factor in the bottom, subtract the 
smaller exponent from the larger exponent.

put the result in the top if the larger exponent was 
in the top and eliminate the factor from the bottom,

or

put the result in the bottom if the larger exponent
was in the bottom and eliminate the factor from the 
top.

But don&#39;t get negative exponents!
Edwin&lt;/pre&gt;</PRE>