It's easiest to find examples that prove the other four choices wrong. For answers A, B, and C, choosing a=2 and b=4 makes the statements incorrect. For answer E, choosing a=4 and b=8 makes the statement false. Answer D is the only one that holds true always.
Either the OE is wrong, or there's a word missing from the question. What's the source? D certainly must be true *if* a and b are *positive* even integers. The question (as posted) only says that they are 'non-zero', which means they could be negative. If a = 2, and b = -2, then a^b = 1/4, and is not an integer, so certainly is not even.
Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.
Private GMAT Tutor based in Toronto