Precedence or powers - Is there more than one way

Question

I'm developing a calculator and I've encountered this issue:

2²²² which power should be calculated first, is there a way this could be solved from the left to the right, meaning 4²² and so on.... I believe that it's wrong, and you should start from the right most power and go down. But I could be wrong...

Answer 1

The standard notation is that if you write it without parentheses then it is evaluated from right to left and you have to use explicit parentheses for a left to right evaluation:

$3^{3^3}=3^{27}$ but $(3^3)^3=27^3$