Final answer:
The GCF of 14x^3 and 35x^4 is 7x^3, which is found by factoring both terms into their prime factors and selecting the highest power of common factors.
Step-by-step explanation:
To find the Greatest Common Factor (GCF) of the terms 14x3 and 35x4, we need to break down each term into its prime factors.
The number 14 can be expressed as 2 x 7, and the number 35 can be expressed as 5 x 7. As for the variables, x3 is x x x, and x4 is x x x x. The GCF is the product of the highest power of common factors in the terms.
Both numbers have a 7 in common, and since x3 is part of both x3 and x4, we can also count x3 as a common factor. Therefore, the GCF of 14x3 and 35x4 is 7x3.
Remembering the properties of exponents, such as the rule xpxq = x(p+q), can make finding the GCF easier. We see that the smaller exponent is the one we use when dealing with the same base during GCF calculations.