SOLUTION: If the products of the integers a, b and c is 1, then what is the difference between the largest and smallest possible values of a^2*b^3*c^4 A)-2 B)-1 C)1 D)2

Algebra ->  Equations -> SOLUTION: If the products of the integers a, b and c is 1, then what is the difference between the largest and smallest possible values of a^2*b^3*c^4 A)-2 B)-1 C)1 D)2      Log On


   

Question 1087349: If the products of the integers a, b and c is 1, then what is the difference between the largest and smallest possible values of
a^2*b^3*c^4
A)-2
B)-1
C)1
D)2
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
2.

Option D).



Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The only integer factors of 1 are +1 and -1.

a^2 and c^4 will be 1 regardless of whether 
a and c are +1 or -1 because even powers of
1 or -1 are always 1.

Any odd power or +1 is +1
Any odd power of -1 is -1  

So the value of a^2*b^3*c^4
depends on whether b is +1 or -1, because the
power of b is 3 which is odd.

The value of a^2*b^3*c^4 is -1 when when b=-1 
and +1 when b=+1.

So the largest value of a^2*b^3*c^4 is +1
and the smallest value of it is -1.

Largest - smallest = 1 - (-1) or
                       1 + 1
which is  -->            2

Edwin