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

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onyebuchinnaji onyebuchinnaji · Answer 2 · 2022-07-15T12:20:35+02:00

The difference between the largest and the smallest possible values is 2.

Product of the integers

a² × b³ × c⁴ = (abc)² ₓ (bc²) = bc²

Given that a,b,c are all integers, and abc = 1

Possible combinations include;

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

Largest case of the combination

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

So bc² = 1

Smallest case of the combination

Smallest case happens when b is -1

So bc² = -1

Difference between the largest case and smallest case

difference = 1-(-1) = 2

Thus, the difference between the largest and the smallest possible values is 2.

Learn more about integers here: https://brainly.com/question/17695139

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