Problem Solving (PS) | If m is an integer such that (-2)^2m = 2^{9 - m}, then m=

SOLUTION

If m is an integer such that \((-2)^{2m} = 2^{9 - m}\), then m=

(A) 1
(B) 2
(C) 3
(D) 4
(E) 6

First of all, since m is an integer, then 2m=even, and therefore \((-2)^{2m}=2^{2m}\).

Sol, we have that \(2^{2m} = 2^{9 - m}\) --> \(2m=9-m\) --> \(m=3\).

Answer: C.