(1) n^m is positive.sud21 wrote:m and n are integers, is m^n an integer?
1) n^m is positive
2) n^m is an integer
If n = -2, m = 2, then n^m = (-2)^2 = 4 and m^n = 2^(-2) = 1/2² = 1/4 = 0.25, not an integer.
If n = 2, m = 2, then n^m = (2)^2 = 4 and m^n = 2^(2) = 4, an integer.
No definite answer; NOT sufficient.
(2) n^m is an integer.
If n = -2, m = 3, then n^m = (-2)^3 = -8 and m^n = 2^(-3) = 1/(2^3) = 1/8 = 0.125, not an integer.
If n = 2, m = 2, then n^m = (2)^2 = 4 and m^n = 2^(2) = 4, an integer.
No definite answer; NOT sufficient.
Combining (1) and (2), n^m is a positive integer. Taking the same examples as in statement 1, again it is NOT sufficient.
The correct answer is E.
