How does Prospero exhibit God-like qualities in the play The Tempest?
Prospero is definitely master of his domain, and in some respects, controls the island on which he and Miranda were shipwrecked as a deity would. One of the most obvious ways Prospero is like a god involves his use of magic to control not only the inhabitants of the island (Ariel and Caliban), but also his ability to make Miranda fall into a deep sleep and enslave Ferdinand.
Be sure to check the eNotes link given below. It gives a great description of Prospero, including the following quote:
"Prospero has been described as godlike in his detachment, doling out punishment and regulating the other characters' perceptions of reality. He has also been compared to Christ for his redemption of the sinful Alonso and his followers."