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
[tex] a^{2}b^{3}c^{4} = (-1)^{2} * 1^{3} * (-1)^{4} = 1 [/tex]
and the smallest number is
[tex] a^{2}b^{3}c^{4} = 1^{2} *(-1)^{3} * 1^{4} = -1 [/tex]
The difference between them is 2.
