Hello everyone, I have stumbled across a curious question while programming.(adsbygoogle = window.adsbygoogle || []).push({});

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 spendnoperations 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.

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# Nested Exponents

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