When I tried to kill a zombie, even though I passed the required power I still couldn't kill it. Why?

Combat power is just a rough estimate. The fact is that there is much more that goes into a battle. Heroes and their skills, research, troop type, and even some buildings such as the war rooms can all affect the outcome of a battle.

If you are having issues killing zombies then you must have a young base. A good mix for me in the early days was using this formation: Fighter, Shooter, Shooter when dealing with zombies. Unlike PvP sieges, zombies only attack your first row, so that's why you want the fighters there to take the hits. Then the shooters in the 2nd and 3rd rows will give you the fire power you need to take them out.