1971 AHSME Problems/Problem 7

Let\ x\ equal\ 2^{-2k} \ From\ this\ we\ get \frac{x}{2}-(\frac{-x}{\frac{-1}{2}})+x\ by\ using\ power\ rule\ Now\ we\ can\ see\ this\ simplies\ to\ \frac{-x}{2}\ Looking\ at\ \frac{x}{2} we\ can\ clearly\ see\ that\ \frac{-x}{2} is\ equal\ to\ -2^{-(2k+1)}\ Thus\ our\ answer\ is\ c