If 12xy^3 + 4x^2y^5 over 4xy^2 is completely simplified to 3x^ay^b + 1x^cy^d, where a, b, c, and d represent integer exponents, what is the value of a?

The first thing to do in this case is to perform the division and then compare with the simplified expression to determine the values of a, b, c and d.
 We have then:
 (12xy ^ 3 + 4x ^ 2y ^ 5) / (4xy ^ 2) =
 3x (1-1) and ^ (3-2) + x ^ (2-1) and ^ (5-2) =
 3x (0) and ^ (1) + x ^ (1) and ^ (3)
 Then, comparing with the simplified expression:
 3x ^ ay ^ b + 1x ^ cy ^ d
 The value of a is
 a = 0
 answer
 the value of a is 0