Question 64756
<pre><font size = 5><b>
Simplify each expression. Use only positive exponents.
(2r^-1 s^2 t^0)^-2 /2rs 
Note: I left a space in the parenthesses so that you 
would know that 2r^-1, s^2 and t^0 are in the 
parenthesses.

{{{ (2r^-1s^2t^0)/(2rs) }}}

Give every factor an exponent of 1 if none shows

{{{ (2^1r^-1s^2t^0)/(2^1r^1s^1) }}}

We divide top and bottom by {{{2^1}}}

{{{ (r^-1s^2t^0)/(r^1s^1) }}}

We know that {{{t^0}}} equals 1, so

{{{ (r^-1s^2*1)/(r^1s^1) }}}

We can dispense with the 1

{{{ (r^-1s^2)/(r^1s^1) }}}

Now we use the rule for getting rid of negative
exponents.  The rules are:

1. If a factor of the numerator has a negative
   exponent, then eliminate base and exponent
   from the numerator, and place a factor which
   has the same base but the opposite signed,
   i.e., positive exponent, as a factor of the
   denominator.

2. If a factor of the denominator has a negative
   exponent, then eliminate base and exponent
   from the denominator, and place a factor which
   has the same base but the opposite signed,
   i.e., positive exponent, as a factor of the 
   numerator. 

We need the first rule to eliminate the {{{r^-1}}}
from the numerator and place {{{r^(1)}}} in the
denominator. 

{{{ (s^2)/(r^1r^1s^1) }}}

Next we add the exponents of r in the denominator, i.e.
{{{r^1r^1}}} = {{{r^(1+1)}}} = {{{r^2}}}


{{{ (s^2)/(r^2s^1) }}}

Finally subtract the exponents of s, 2-1 = 1,

{{{ (s^1)/(r^2) }}}

or just

{{{s/r^2}}}

Edwin</pre>