(R^c)(R^d)(R^e) = R^(-12). If R0, and c, d, and e are each different

Question

(R^c)(R^d)(R^e) = R^{(-12)} . If R > 0, and c, d, and e are each different negative integers, what is the smallest that c could be?

A. -12 
B. -10 
C. -9 
D. -6 
E. -1

BrentGMATPrepNow · Answer

If we let  R = 1 , then  c ,  d  and  e  can have  any  value.

For example, if  R = 1 , then it could be the case that  c = -100 ,  d = -90  and  e = -80 , since it's true that  (1^{-100})(1^{-90})(1^{-80}) = 1^{(-12)}

Charli08 · Answer

Rule of exponents:

(R^c)(R^d)(R^e)= R^(c+d+e)

Question stem: what is the smallest number c can be, when  c,d,e are all distinct negative values
 
(R^c)(R^d)(R^e)= R^-12

==> c+d+e = -12

c = -9
d= -2
e=-1

c + d + e = -12

==>  C

Raben · Answer

Hi,

I agree for the most part, but how do we know that c isn't -1 in this case? Wouldn't it also add up to 12?

Charli08 · Answer

You mean if c = -1 and e = -9? Assuming this is what you meant it would work in general however it says that "c is the smallest number" in the question stem. Hope this helps!

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(R^c)(R^d)(R^e) = R^(-12). If R>0, and c, d, and e are each different

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