Use the direct superscript/subscript format options. You can find these on the … menu after selecting some text, or you can press Ctrl+Shift+. and Ctrl+Shift+, respectively (Cmd+Opt+. and Cmd+Opt+, on a Mac).

This method is convenient if you have some very simple math or chemical formulas, or are using the superscripts or subscripts for footnotes or other non-mathematical purposes.
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Use LaTeX equations. For more complicated math, you'll get much nicer formatting for both your superscripts/subscripts and the rest of your equation by using LaTeX. Type $$ to start entering a LaTeX equation.
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See Writing Equations with LaTeX for a detailed treatment of this feature.

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