Question

If the product of the integers a, b, and c is 1, then what is the difference between the largest and the smallest possible values of $a^{2} * b^{3} * c^{4}$?
A: -2
B: -1
C: 1
D: 2

Answer 1

We have given that all three of these numbers are integers and the product is one. From this fact, we can deduce that this numbers are 1 and -1. When we put these numbers into the second product, we find that largest number is

$a^{2}b^{3}c^{4} = (-1)^{2} * 1^{3} * (-1)^{4} = 1$

and the smallest number is

$a^{2}b^{3}c^{4} = 1^{2} *(-1)^{3} * 1^{4} = -1$

The difference between them is 2.