To be more precise you have 2 options - set the activity to "leave unused devices on" or simply add the equipment you want left on to the other activities. Or the 3rd option is to leave equipment on all the time.

equipment should be left on all the time - set the device's power buttons to "leave this device on all the time"
equipment should turn on when the first activity is selected and off when you hit the OFF button - add the device to all activities (or set all activities to "leave unused devices on")
equipment should only turn on and stay on for selected activities - add the device to the activities where you want it to stay on