Problem:
Let r be the number that results when both the base and the exponent of ab are tripled, where a,b>0. If r equals the product of ab and xb where x>0, then x=
Answer Choices:
A. 3
B. 3a2
C. 27a2
D. 2a3b
E. 3a2b
Solution:
Since r=(3a)3b=((3a)3)b=(27a3)b, and r=abxb=(ax)b, we have (27a3)b=(ax)b. Thus 27a3=ax, which we solve to obtain x=27a2. To show that none of the other choices is correct, let a=b=1.