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## Main Question or Discussion Point

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: α

Nesting that in an exponent is a simple operation and a common occurrence: α

(α

But then I run into a problem when I nest this number with yet another exponent: α

See, the exponent for me is calculated from right to left, so I can't simply store α

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

Thanks for your time.

To start the process, say I have a a positive integer greater than one: α

_{0}Nesting that in an exponent is a simple operation and a common occurrence: α

_{0}^{α1}(α

_{1}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: α

_{0}^{α1α2}See, the exponent for me is calculated from right to left, so I can't simply store α

_{0}^{α1}into memory and then set that to the α_{2}power, because that only works on operators that are calculated left to right.**So my question is this: Given a chain of nested exponents α**_{0}^{α1α2...αn}, is there a closed form means to determine α_{0}^{α1α2...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.