Find the greatest common divisor of the term 144x^3y^2 and 81xy^4?

To find the greatest common divisor of the terms 144x^3y^2 and 81xy^4, we need to factorize both terms and then find the common factors.

Factorizing 144x^3y^2:
144 = 2^4 * 3^2
x^3
y^2

Factorizing 81xy^4:
81 = 3^4
x
y^4

Now, we can find the common factors between the two terms:
Common factors:
3^2 (from 144 and 81)
x (from both terms)
y^2 (from both terms)

Therefore, the greatest common divisor of the terms 144x^3y^2 and 81xy^4 is 3^2 * x * y^2 = 9xy^2.