Don't install a regular splitter between the power supply and the pre-amp or you will short circuit the system and it won't work. You can install a special splitter that is power passive on only one port. Or put a DC Block on the outputs that don't run to the power supply. Also you can't put any type of matching transformers between the power supply and the pre-amp. In areas with very weak signals you would need to use a pre-amplifier first to boost the signal levels up to a point where they can be distributed.
Distribution amplifiers are available in many configurations.
There are distribution amps designed to cover just off air frequencies and those designed to cover off air and cable frequencies.