Here's how it breaks down:
* an-: meaning "without" or "lacking"
* arch-: meaning "leader" or "ruler"
Therefore, anarch- means "without a leader."
This root is found in words like:
* anarchy: a state of disorder due to the absence of government or control.
* anarchist: a person who believes in or advocates for anarchy.
* anarchic: characterized by disorder and lack of control.