Final answer:
The greatest common monomial factor of 8xy^(3) and 60y is 4y.
Step-by-step explanation:
To find the greatest common monomial factor of 8xy^(3) and 60y, we need to determine the largest term that both expressions have in common. Let's break down the terms into their prime factors:
8xy^(3) = 2 * 2 * 2 * x * y * y * y
60y = 2 * 2 * 3 * 5 * y
The common factors are 2 * 2 = 4 and y. Therefore, the greatest common monomial factor is 4y.