How turn offf LOGITEC Z5500?

The setup guide shows there is a power button (that toggles between on and standby) on the front of the control unit AND on the remote. You may be making a distinction between "standby" and total shutdown. Normally you would leave them on standby, but if you want to turn them off completely simply plug the power cord into a switched power bar (better yet a switched surge protector ... which you should always use with electronic equipment) and use the switch on the bar.