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One of the basic (and frequently used) properties of cardinal exponentiation is that $(a^b)^c=a^{bc}$.

What is the proof of this fact?

As Arturo pointed out in his comment, in computer science this is called currying.

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    I thought that this result appears quite frequently in various questions as an auxiliary computation, so it would be good to have something to refer to. I've asked moderator to make this community wiki. (Sorry if I have overlooked a similar question.)2011-08-14
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    Computer scientists know this (though they perhaps are unaware of it) as [currying](http://en.wikipedia.org/wiki/Currying).2011-08-14

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