Final answer:
To find the GCF of 6x⁵y⁷ and 8xy⁸, we find the largest number that divides both 6 and 8, which is 2, and the highest power of x and y that occurs in both expressions, which is x and y⁵, respectively. Therefore, the GCF is 2xy⁵.
Step-by-step explanation:
To find the greatest common factor (GCF) of the expressions 6x⁵y⁷ and 8xy⁸, we need to determine the highest power of each variable that is present in both terms and the largest number that divides both numerical coefficients.
Looking at the numerical coefficients, the GCF of 6 and 8 is 2 since it is the largest number that can divide both without leaving a remainder. Next, for variable x, x is the highest power present in both expressions. Lastly, for variable y, y⁵ is the highest power present in the expression 6x⁵y⁷ that also occurs in the term 8xy⁸.
Combining these together, the GCF is 2xy⁵.
The correct answer is option (a) 2xy⁵