"I like this exhibition."
Translation:Мне нравится эта выставка.
I am going to answer my question before I have posted it. I think that "This exhibition pleases me" means that the exhibition is the subject of the verb and is therefore nominative whereas in "I like this exhibition" "I" is the subject, "Exhibition" is the direct object and therefore would be in the accusative. So "мне нравитса эта выставка" but "я люблю эту выставку". So the question was "Why is exhibition in the nominative?".
Thank you mightypotatoe