Final answer:
The GCF of xy^10, x^4 y^6, x^9 y^9, and x^10 y^10 is x^4 y^6.
Step-by-step explanation:
The GCF (Greatest Common Factor) is the largest number that divides evenly into each of the given terms. In this case, we are dealing with terms that contain variables raised to different powers. To find the GCF, we need to look for the highest power of each variable that appears in all the terms.
Let's break down each term into its prime factors:
- xy10 = x * y10
- x4y6 = x4 * y6
- x9y9 = x9 * y9
- x10y10 = x10 * y10
Now, let's identify the highest power of each variable that appears in all the terms:
- x: the highest power is x4
- y: the highest power is y6
Therefore, the GCF of xy10 , x4y6 , x9y9 , and x10y10 is x4y6.