Final answer:
The greatest common factor (GCF) between the expressions a²b⁵ and a³ is a², because we choose the smallest exponent of 'a' that is in both expressions.
Step-by-step explanation:
To find the greatest common factor (GCF) between the expressions a²b⁵ and a³, we need to identify the highest exponent of 'a' that is common to both expressions. In a²b⁵, the exponent for 'a' is 2, and in a³, the exponent for 'a' is 3.
We look for the lowest power of 'a', which is a². The variable 'b' does not appear in the second expression, thus it is not considered in the GCF. Therefore, the GCF of a²b⁵ and a³ is a².
Remember, when looking for a GCF that involves exponents, you only need to consider the variable's smallest exponent that appears in all terms involved.