Final answer:
The GCF of x¹⁹y⁷, x⁷y⁷, and x⁴y² is x⁴y² since these are the smallest powers of x and y common to all terms.
Step-by-step explanation:
To find the Greatest Common Factor (GCF) of the given list of terms x¹⁹y⁷, x⁷y⁷, x⁴y², we need to identify the highest powers of x and y that are common to all terms. The smallest power of x in the list is x⁴ and the smallest power of y is y². Therefore, the GCF of the given list is x⁴y².
A step-by-step explanation would involve:
- Listing out the factors of each term.
- Comparing the factors to find the highest power of x and y that appears in all three terms.
- Identifying x⁴ as the greatest power of x common to all terms and y² as the greatest power of y common to all terms.
In conclusion, the GCF of x¹⁹y⁷, x⁷y⁷, and x⁴y² is x⁴y².