Parentheses in Power Tower

Algebra Level 2

Suppose we start with a number 22. Trivially, no matter the number of parentheses, the result is still 22.

Squaring that, we have 222^2. Then, the results are the same for any choice of parentheses.

For three 22's, wherever the parentheses are set, the result is 1616. For instance, (22)2=2(22)(2^2)^2 = 2^{(2^2)}.

What about the power tower of at least four 22's? Would the result still be the same for any choice of parentheses and for all number of 22's?

Note: Order of operations holds.


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