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.
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