Problem: Given the binary operation* defined by a∗b=ab for all positive numbers a and b. Then for all positive a,b,c,n, we have
Answer Choices:
A. a∗b=b∗a
B. a∗(b∗c)=(a∗b)∗c
C. (a∗ bn)=(a∗n)∗ b
D. (a∗ b)n=a∗(bn)
E. None of these
Solution:
(a∗b)n=abn and a∗(bn)=abn.