If x is odd, then 2^x + 3^x is also odd

[epkid08]

Homework Statement

Prove: If x is a positive odd integer, then $$2^x + 3^x$$ is also a positive odd integer.

The Attempt at a Solution

Assume x is odd; there exists an integer k such that x = 2k + 1. Then
$$2^x + 3^x = 2^{2k+1} + 3^{2k+1}$$

I don't know how to go about simplifying it from here.

 

[Dick]

Is 2^x even or odd? What about 3^x? I'm a bit confused why they are specifying x odd. Isn't it true even if x is even?