I'm considering writing the following in an email to a friend.
I'm sure the exam'll be easy.
But it just sounds wrong to me, even in an informal setting....
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People do speak like this. How you wrote it is correctly spelled.
It's helpful to put this in the same category as slang - you do not want to write it this way in professional or formal writing.
An author of in a book of fiction (or a comic book)P may do this, where the author is writing how people talk, but you wouldn't see this outside of that context normally.