Step 1: The conjugate base of an acid is formed by removing a proton (H\(^+\)) from the acid. In this case, the acid is \( {(CH}_3{)}_2{NH}_2^+ \).
Step 2: By removing a proton from \( {(CH}_3{)}_2{NH}_2^+ \), the conjugate base is \( {(CH}_3{)}_2{NH} \), which is a neutral species.
Step 3: Thus, the correct answer is \( {(CH}_3{)}_2{NH} \).