A:Answer Your question is not clear when you use the terms "plug in" or "power it". I'll still try to answer.
1) The sound bar has an internal amplifier, so no external amplifier is needed.
2) The sound bar has a AC plug that must be connected to a 110V (US) wall outlet to power the amplifier in the sound bar. See manual, page 9 : http://cdn.vizio.com/misc/KBImages/models/m21dh8/manual.pdf
3) The sound bar several ways to get the audio signal from the source (TV). If your TV has an HDMI ARC port and that is used to plug into the sound bar, then the sound bar volume and power will be controlled by the TV. So, when you turn up the volume of the TV, the sound bar volume will go up. Additionally, if you turn on/off the TV, the sound bar will be turned on/off. This last feature is part of why the "power it" term is a little confusing.
4) I don't know if cable boxes have HDMI ARC features (I suspect not) so it is not likely you will want to connect the cable box directly to the sound bar. That is OK though. If you connect the sound bar to the TV, whatever sound that would normally come out of the TV speakers will come out of the sound bar.