This site http://what-if.xkcd.com/14/ states that during a helium flash, "the reaction rate is proportional to the 40th power of the temperature".
Taking for granted that this is true, how can such a large exponent arise in a physic equation? It just makes no sense to me that some physical process could give rise to this phenomenon.
An explanation of how it can arise for a helium flash would be satisfactory, but the question is really more general. How can a physical process accumulate enough factors to get up to x^40? Thermodynamic processes tend to be in the x^2 or x^3's and geometry can only add a few more x^3's.
Note that we are not talking about the scale of things (obviously the 40th power is not a big deal in the length or time scales), we are talking about a physics /equation/.