a3/2b3c5
—————————
  a2b1/3

 a3/2b3c5
——————————
  a2b1/3

To divide exponentials with like bases and positive exponents,
subtract their exponents, larger minus smaller, placing the
common base with the difference exponent in the numerator or
denominator, depending on which the larger exponent is in.

a2 has a larger exponent than a3/2 so we subtract exponents
2 - 3/2 = 4/2 - 3/2 = 1/2 and since a2 has the larger 
exponent and is in the denominator, we place a1/2 in the
denominator and eliminate the a3/2 and the a2:

   b3c5
——————————
 a1/2b1/3
 
b3 has a larger exponent than b1/3 so we subtract exponents
3 - 1/3 = 9/3 - 1/3 = 8/3 and since b3 has the larger 
exponent and is in the numerator, we place b8/3 in the
numerator and eliminate the b3 and the b1/3:

   b8/3c5
——————————
    a1/2

Edwin
AnlytcPhil@aol.com