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2002 AMC 12A Question 3

AMC12 · 2002 AMC 12A

Question 3

According to the standard convention for exponentiation, $$
2^{2^{2^2}} = 2^{\left(2^{\left(2^2\right)}\right)} = 2^{16} = 65{,}536.
$$ If the order in which the exponentiations are performed is changed, how many other values are possible?
  1. $0$
  2. $1$
  3. $2$
  4. $3$
  5. $4$