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1970 AMC 12 Question 13

AMC12 · 1970 AMC 12

Question 13

Given the binary operation $*$ defined by $a*b=a^b$ for all positive numbers $a$ and $b.$ Then for all positive $a,$ $b,$ $c,$ $n,$ we have:
  1. $a*b=b*a$
  2. $a*(b*c)=(a*b)*c$
  3. $a*(b^n)=(a*n)*b$
  4. $(a*b)^n=a*(bn)$
  5. None of these