Iterated Powers
As we can see from the definition, when evaluating tetration expressed as an "exponentiation tower", the exponentiation is done at the deepest level first (in the notation, at the highest level). In other words:
Note that exponentiation is not associative, so evaluating the expression in the other order will lead to a different answer:
Thus, the exponential towers must be evaluated from top to bottom (or right to left). Computer programmers refer to this choice as right-associative.
When a and 10 are coprime, we can compute the last m decimal digits of using Euler's theorem.
Read more about this topic: Tetration
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