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.


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