No matter which natural number "n" that you choose, explain why the following statement can never be true: 2^n + 3^n = 4^n

First of all, 2^n and 3^n are exponentials with different bases, and thus their sum cannot be simplified beyond 2^n + 3^n.  In other words, these two functions cannot be combined ino one function (such as 4^n).

You may gain much more insight by graphing 2^n, 3^n and 4^n to determine whether there is truth in the given statement or not.