How do I punctuate a sentence in parentheses that follows another sentence?

Note: This post relates to content in the eighth edition of the MLA Handbook. For up-to-date guidance, see the ninth edition of the MLA Handbook.

If a sentence in parentheses follows a sentence, place a period before the closing parenthesis:

I went to an exhibit at Vito Schnabel’s gallery. (Vito is the son of the artist Julian Schnabel.)

If a phrase or clause in parentheses concludes a sentence, place a period after the closing parenthesis:

I went to an exhibit at the gallery of Vito Schnabel (son of the artist Julian Schnabel).

I went to an exhibit at the gallery of Vito Schnabel (who was the son of the artist Julian Schnabel).