How does authority and power relate?

Authority can use either law or power depending on the circumstances. An authority who uses power outrageously is not acting properly.

On this question, when the Word "authority" is mentioned along with "power" I assume that "authority" is related to the police affairs. But authority is also related to any person who works in any other governamental department. In this case, power differs from that kind of power used to maintain order in society issues.