Use the adverb exceedingly to mean "very." You might brag, for example, that you did exceedingly well on the big math test last week.
Exceedingly means "to a very large degree," so it's best to save it for things that really need to be emphasized. You might be exceedingly angry at your little sister after she borrowed your favorite sweater and spilled ketchup on it, or exceedingly happy to have gotten into your first choice college. Exceedingly has a Latin root, excedere, "depart, go beyond, be in excess, or surpass."