Hello everyone, I have stumbled across a curious question while programming. To start the process, say I have a a positive integer greater than one: α0 Nesting that in an exponent is a simple operation and a common occurrence: α0α1 (α1 is also a positive integer greater than 1. In fact, all numbers mentioned in this problem of mine are in that given set) But then I run into a problem when I nest this number with yet another exponent: α0α1α2 See, the exponent for me is calculated from right to left, so I can't simply store α0α1 into memory and then set that to the α2 power, because that only works on operators that are calculated left to right. So my question is this: Given a chain of nested exponents α0α1α2...αn, is there a closed form means to determine α0α1α2...αnαn+1 without having to recalculate the exponents from right to left? I apologize if this is the wrong place to ask, but as a programmer, nested exponents are causing me a headache, because I have to spend n operations to calculate the nested exponent every time I nest it. While not completely slow, I would enjoy a faster means of computing this. I am also aware my question might not seem completely clear, so please ask for clarifications if you require any. Thanks for your time.