Unfortunately, you'll have to learn the differences by rote. "Wake" and "rouse" are synonyms (as verbs), but "awake" and "arouse" have very different meanings; "awake" is an adjective, while "arouse" is a verb. If the word is of Greek origin, "a" or "an" means "without".
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guzhao67 wake and awake, rouse and arouseThe verbs with the "a" prefix usually have more abstract meanings than the verbs without "a". Consider these examples: