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

Since there are no multiples other than 1 and -1 that could multiply in any way to equal 1, those are the only numbers you can really work with

it is a possibility that a, b, and c could equal 1 but then it would go wrong when comes time to subtract since all numbers are equal and cannot subtract largest from smallest.

a logical approach would be to try -1, -1, and 1 since -1 * -1 = 1 and then 1* 1 =1

we can make a= -1 , b= -1, and c= 1
 (we need b to equal -1 so that we get an answer of -1 opposed to if we made a=-1 and c=-1, all outcomes would equal 1)
-1²=1
-1³=-1
1⁴= 1
since 1 is the largest possible outcome and -1 is the lowest possible outcome you should subtract the two

1-(-1) = 1+1 = 2

The answer should be D: 2
 
hoped this helped at all!