Puzzle: estimate this number!

If you're good at math, you can do this by just thinking.  If you're not, you can use a calculator and see what you get.  But in that case, beware: a 'tower of powers' like this:

x^x^x^x^x

means

x^(x^(x^x))

not

((x^x)^x)^x

I'm asking about the first sort of thing.
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