Conceivably derived from "exactamente," Spanish for "exactly."
It is used primarily by U.S. non-Spanish speakers. The Fonz, a hip irreverent character on the 50s TV show The Happy Days is responsible for some of the earliest recorded utterances though it's likely to have been in use before then.
The second half of the world "mundo," possibly results from mishearing exactamente and, in another context, mundo, "world" in Spanish. Interestingly the understood meaning has nothing to do with the meaning "world." Even so in Spanish it might translate as "exact world," though the gender of "exacta" renders the phrase grammatically correct.