Correct spelling, explanation: exhibit is a word of Latin origin, exhibere. This is very important, as the word was built by adding the prefix ex- to the base word hibere which allows us to work out the meaning of exhibit based on the original word.

Definition of exhibit:
noun
1. a display of something
We went to the zoo and spent a lot of time looking at the monkey exhibit.
verb
2. to display something
I always stop by the local bakery; they exhibit their cakes in the window, and I always end up buying something tasty.
3. to show signs of something
At the end of the football match, most players exhibit signs of exhaustion.

Incorrect spelling, explanation: the pronunciation of exibit may be believable, but it is not correct. The reason why it can’t be correct is that the word exhibit comes from the Latin exhibere and this needs to be reflected in the current English word. Sure, the word exhibit has already undergone some changes, but the basic construction always has to be kept in place.