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Simplify a nested math function

I'm trying to simplifiy this nested math function:

V = a1 * (1 - (1/(1+10^(1/b1))^(1/(1+10^(1/b2)))^...))

where a1, b1, b2, a2, etc, are different constants and V is what I want to maximize.

Any ideas?

Thanks!

EDIT: I can't just take the root of the terms as I have to optimize V every time I run the program so I'll have to do it numerically and I'd like to avoid the run time calculation

A:

The root of your function is

\begin{align*}

\frac{V}{a1} &= \frac{a1}{a1} \cdot \left(1 - \frac{1}{\left(1 + 10^\frac{1}{b1}\right)^\frac{1}{a1}}\right) \cdot \left(1 - \frac{1}{\left(1 + 10^\frac{1}{b2}\right)^\frac{1}{a1}}\right)\cdots \\ 0b46394aab

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