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 …

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.