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2002 AMC 10A Question 3

AMC10 · 2002 AMC 10A

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. $4$