First, we can simplify the expression inside the parentheses by dividing both the numerator and the denominator by their greatest common factor, which is 8a^2b^2:
(8a^3b^2/16a^2b^3) = (a/2b)
Now, we can substitute this expression back into the original expression and simplify:
(8a^3b^2/16a^2b^3)^4 = [(a/2b)^4] ^4
= (a^4/16b^4) ^4
= a^16/16^4b^16
= a^16/65536b^16
Therefore, the simplified expression is a^16/65536b^16.