Parentheses in Power Tower
Algebra
Level
2
Suppose we start with a number \(2\). Trivially, no matter the number of parentheses, the result is still \(2\).
Squaring that, we have \(2^2\). Then, the results are the same for any choice of parentheses.
For three \(2\)'s, wherever the parentheses are set, the result is \(16\). For instance, \((2^2)^2 = 2^{(2^2)}\).
What about the power tower of at least four \(2\)'s? Would the result still be the same for any choice of parentheses and for all number of \(2\)'s?
Note: Order of operations holds.
by
Michael Huang