Final answer:
The greatest common factor between x⁴ and x⁶ is x⁴, since it is the highest power of x that divides both expressions without any remainder.
Step-by-step explanation:
The greatest common factor (GCF) between x⁴ and x⁶ can be determined by finding the highest exponent that both terms share. Since the key rule for powers is that xp × xq = x(p+q), the same principle applies in reverse for finding the GCF, where we look for the highest power of x that divides both expressions.
In this case, we have x⁴ (x × x × x × x) and x⁶ (x × x × x × x × x × x). As such, x⁴ is the GCF since x⁴ is contained completely in x⁶ without any remainder. Therefore, the GCF of x⁴ and x⁶ is x⁴.