Manhattan Challenge Problem of the week! - sept 4

The Power of Absolutes

If a and b are integers and a is not equal to b, is ab > 0?

(1) a^b > 0

(2) a^b is a non-zero integer

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.