Shakespeare: The Tempest

So in class we talked about what powers does Prospero really have? When reading the first two scenes of The Tempest, it doesn't seem like Prospero is as powerful as we all thought he was in class. After looking back at the play, it seems like Prospero's power mostly comes from Ariel. The storm that wrecked the boat was conjured up by Ariel it seems, and so far that is the only real power we have seen. Yes he does have a sleep spell of some sort, but that does not seem to be that powerful as Miranda woke up from it kind of quickly it seemed like. And this "power over Ariel" is not magic at all. Or at least no magic that he showed. When Ariel complains and Prospero threatens her, he simply states that she should be grateful that he rescued her from that tree, and if she is not then he would put her back in the tree. But who is to say he didn't just take an ax to the tree? Like I can say I will put you in a tree, but that doesn't mean I actually have the power to do it. Maybe he would have forced Caliban to put her in the tree, they don't really talk about if Caliban has any magic powers, but if he was the son of a witch he has to be somewhat magical right? Which leads back to Prospero's magic over Caliban. It says Prospero took Caliban in when he was young since his mother (The witch Sycorax) died. But it doesnt say he uses magic to keep Caliban as a slave, just that he is Prospero's slave. To me it just seems that Prospero is all talk and very little show. But this may change as we read further into the play, or it may not. As we should all remember this is a play and back then they didnt have special effects to show the magic, so Shakespeare very well may have just made Prospero all talk and no show to fit what a play could show.