which one is larger?
think about it in this way
e^pi vs pi^e
=> pi*ln(e) vs e*ln(pi)
=> ln(e)/e vs ln(pi)/pi
then think about the properity of the function ln(x)/x,
which maximized at x=e, so we have
ln(e)/e > ln(pi)/pi
=> e^pi > pi^e
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