The Comparison of Values of the Numbers pi^[e^pi]n Versus e^[pi^e]n and e^(pi^[e^pi]n) Versus pi^(e^[pi^e]n)

Abstract

This research is based on the fact that researchers have studied the proofs of the comparison of the values of  e^pi  and pi^e by using the mathematical proof, without calculating them. It was proved that  e^pi > pi^e.  

In this study, researchers compare the values of   pi^[e^pi]n versus e^[pi^e]n and e^(pi^[e^pi]n) versus pi^(e^[pi^e]n) by using the mathematical proof. We show that if the number of exponents is even, then e^(pi^[e^pi]n) is greater than pi^(e^[pi^e]n). On the other hand, if the number of exponents is odd, we obtained  pi^[e^pi]n is greater than e^[pi^e]n. Moreover, researchers analyze the results of this research.