souvonik2k wrote:

If \(R^a*R^b*R^c=R^{-9}\) and if R>0 and a,b and c are each different negative integers, what is the smallest that c could be?

A) -1

B) -2

C) -6

D) -7

E) Cannot be determined

The trap in this question is "smallest."

It almost got me; I decided that "-1" was too obvious. The smallest negative variable/ number is the one most to the left on the number line.

When bases are the same (here, R), add exponents. Sum = -9

a + b + c = -9

c = 9 - a - b

a and b are different negative integers. To minimize c, to make it farthest to the left of 0, maximize a and b -- make them, going left from zero, as close to 0 as possible.

a = -1

b = -2

c = 9 - a - b

c = 9 - (-1) - (-2) = (-9 + 1 + 2) =

-6Answer C

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