If the product of the integers a, b, c is 1, then what is the difference between the largest and the smallest possible values of a^2xb^3xc^4

Given that: abc = 1

a^2*b^3*c^4 = (abc) ^2 * (bc^2) = bc^2

Since a, b, c are all integers, here are the possible combinations

(1,1,1) and (1,-1,-1)

So, the largest case happens when b and c are both 1, or b is 1, c is - 1

So bc^2 = 1

Smallest case happens when b is - 1

So bc^2 = - 1

So the difference will be 1 - (-1) = 2