Does the choice band affect the ability 'Technician' when using a move such as Mach Punch (with 40 attack power)?
Mach Punch will get boosted by Technician to a power of 60, then again by the Choice Band to a power of 90. Technician will take effect even after the effects of Choice Band though.
40 times STAB (1.5) is 60, x Technician is 120, add Choice Band (1.5) is 180.