# Nested Exponents

## 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: α0
Nesting that in an exponent is a simple operation and a common occurrence: α0α1
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: 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.

symbolipoint
Homework Helper
Gold Member
Try reviewing rules of exponents using some simple example.

Find $2^{{3}^{2}^{5}}$. Try doing the exponents from right to left; and also try doing from left to right. See what results.

format tags not working right. 2^3^2^5
Using TexAide: $$2^{3^{2^5 } }$$

[STRIKE]Should be the same as $2^{3*2*5}$[/STRIKE]Obviuos mistake. That would not be result of the nesting. See next member's post.

Last edited:
rcgldr
Homework Helper
Try reviewing rules of exponents using some simple example.
By nesting the OP means 2^(3^4) = 2^81 = 2417851639229258349412352, this is different than (2^3)^4 = 8^4 = 4096.