consider e^x vs. x^e first. Take ln of each value, we get x and e*ln(x). if x-e*ln(x)>0 when x=pi, then e^pi is bigger. diff x-e*ln(x) against x, we have 1-e/x, when x=e, x-e*ln(x) has minimum value which is 0, since pi>e, therefore x-e*ln(x)>0 when x=pi. So e^pi is bigger!!!