Suppose we start with a number . Trivially, no matter the number of parentheses, the result is still .
Squaring that, we have . Then, the results are the same for any choice of parentheses.
For three 's, wherever the parentheses are set, the result is . For instance, .
What about the power tower of at least four 's? Would the result still be the same for any choice of parentheses and for all number of 's?
Note: Order of operations holds.