SOLUTION: <pre><b> 54x⁶y^-4z² ----------- 9x^-3y²z^-4</pre>

 54x6y-4z2
------------
 9x-3y2z-4

Rule 1: If a negative exponential is a factor of the numerator,
move it from numerator to denominator and change the sign of the
exponent

Rule 2: If a negative exponential is a factor of the denominator, 
move it from denominator to numerator and change the sign of the 
exponent


 54x6y-4z2
------------
 9x-3y2z-4 

Since the x6 already has a positive exponent, leave it where it is.
Move the y-4 to the denominator and change the sign of the -4 
exponent to +4

   54x6z2
------------
 9x-3y2z-4y4

Move the x-3 to the numerator and change the sign of the -3 exponent
to +3

 54x6z2x3
----------
 9y2z-4y4

Move the z-4 to the numerator and change the sign of the -4 exponent
to +4

 54x6z2x3z4
------------
   9y2y4

Now that all exponents are positive, add the exponents of x6 and x3, 
getting x9

  54x9z2z4
------------
   9y2y4

Add the exponents of z2 and z4, getting z6

  54x9z6
----------
   9y2y4

Add the exponents of y2 and y4, getting y6

  54x9z6
----------
    9y6

Divide the numerator and denominator by 9

  6x9z6
---------
    y6

Edwin
AnlytcPhil@aol.com