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Superscript
Math & Science
Superscript is especially common in scientific formulas and mathematical expressions. E=mc^2, where '2' is in superscript.
Not For Emphasis
Superscript isn't used for emphasizing text; that's what bold or italics are for. 
Ordinals In Text
Use superscript for ordinal indicators in dates and numbers in non-technical writing. She was born on January 1^st^ and he on the 2^nd^.