Power is concentrated among a few people, and your relationship with that person matters a lot more than your title.
Accordingly, there are few rules and not much bureaucracy in a Power Culture because whatever the Chief says, that's the law. Very early stage startups with charismatic leaders tend to be Power Cultures, but you'll find them in other types of organizations as well. Fashion, publishing, and film come to mind. In fact, "The Devil Wears Prada" and the documentary "The November Issue" are perfect depictions of Power Cultures. Apple under Steve Jobs and the early days of Facebook were Power Cultures. Since access to the leader(s) means so much, you can expect a lot of jockeying to be the Chief's BFF.
The advantage of a Power Culture is that decisions can be made very quickly. However, the calibre of the decision maker directly affects the quality of the decisions made. You have to believe in the infallibility of the leader in a Power Culture or you'll be miserable.
You'll flourish in a Power Culture if you make relationships easily, can work in an less-structured environment, and don't mind (or actually enjoy) the political wrangling.
Would this culture be a good fit for you? Take this quick assessment to find out.