first off despite the fact that you might use the same word---power---to designate a relation or pattern in any number of situations, power is not really one thing. you could say that power is a type of dominance that relies on assymetry of force that in some abstract sense can be linked back to the potential for violence--but it is not obvious that this says much simply because i am not sure that it is so easy peasy to separate "power" from the modes through which it is exercised. violence then becomes a subset of the term power, and what it means is a function. power is linked to the routines of its exercise and the framework (legal or convention or otherwise) that legitimates it/outlines it on the one hand, and the systems of institutions that are developed--and both these general characteristics are, taken together, basic to political power--as is the legal or political framework that orients these institutions and legitimates the apparatus as a whole. so power and legitimation are tied every bit as closely as power and violence. all these seem to me to be mutually defining terms.
for example: modern state power is often understood as *routinized* violence. the routinization---via bureaucracy say, or more obviously through law---is a sublimation of violence.
depending on the legal and political context, you can easily imagine situations in which the breakdown of this routinization leads to direct use of violence leads to a breakdown of legitimacy of the state itself. a simple example: the photograph of the kent state student shot by the national guard in 1969 (i think)...you know the photograph, i expect:
so if you use this photo to think about the question posed in the op---in this instance, the state exercised violence--and not its police function (say)--because the act itself violated the rules--and so was delegitimating of the state. it is possible that, from a different political viewpoint, there was no violence at kent state, only the legitimate actions of the national guard. so the notion of violence floats in and out of your interpretation of the photograph.
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the idea that violence stands above the routines that shape it does seem to come from machiavelli---but it is strange that this would be the case, if you think about it.
you could say that just as machiavelli's work instituted the notion of the political itself (rather "the prince" is the text around which the instituted notion of the political as a category took shape), it follows that the notion of the political duplicates the logic of various readings of "the prince"--many of which use it to effectively detach the notion of violence from having and holding power from any particular routine of exercising power.
but if you think about this, i think it's clear that the scenario of conquest (which is the basic scenario addressed in that book) is itself a situation. so the prince doesn't describe the basis for ALL situations--rather it is about the fundamental role played by situation itself. so you cant move from the prince to a general theory of violence and its relation to power---you move from violence to the problem of stabilization and the development of routines as the basis for power. getting power is one set of question: exercising it another.
what the "the prince" is mostly directly about is not violence, but the notion of situation itself: the situation of conquest or invasion and how a prince would go about managing its particular complexities--so you could say the same thing about it--violence is not the same as power, but its crude precondition *in the situations that machiavelli addresses*
power is implied by the way it is exercised--so it is situational or frame-contingent--so in the prince, the situation of having-conquered another community places, you, mister prince, by definition outside the routines----and your problem, really, is establishing legitimacy long enough to be able to set up new routines based around a different center. which of course is you.
sometimes i think people are so fascinated by the prince because while they are reading it, they are addressed as if they *are* the prince and there is something flattering in that, isnt there?
anyway in *that situation* power is violence but its exercise is about stabilization. but the next step is obvious: without successful routinization, there is no power. there is only the after-image of violence. that is not power.
and this is a situation amongst a host of them, and is not a meta-situation (one that outlines the logic of others).
you could say that political power, then, is both the potential for violence and the routines that channel it/transform it--and that one only has meaning in terms of the other.
so let's see---violence can only be deployed as power through its routinization.
routinized violence is a way of seeing the ways in which state power is exercised--but its sources lay in the routine itself and the legitimacy of the institutions that enact it and the framework that orients the political system as a whole.
so i dont see how you can detach violence from its routinization and questions of legitimacy if you are thinking about political power.
at this point, the post dovetails with what the other rb and jj posted above.
this is written through my 3rd cup of morning coffee, so any logic lapses are early morning products yes.