To exult is to be extremely joyful whereas to exalt is to raise something in esteem or power or to intensify something. The adjectival forms are “exultant” and “exalted.”

Something supremely admirable has exalted status.

People who have celebrated with great joy about an event have exulted in it. The spelling “exulted” should be used only for the past tense of the verb “exult”: “The candidate exulted in her victory.”