Use the <sup></sup>tag (<sub></sub> is the equivalent for subscripts). See this gist for an example.
The universal solution is using the HTML tag <sup>, as suggested in the main answer.
However, the idea behind Markdown is precisely to avoid the use of such tags:
The document should look nice as plain text, not only when rendered.
Another answer proposes using Unicode characters, which makes the document look nice as a plain text document but could reduce compatibility.
Finally, I would like to remember the simplest solution for some documents: the character ^.
Some Markdown implementation (e.g. MacDown in macOS) interprets the caret as an instruction for superscript.
Ex.
Sin^2 + Cos^2 = 1
Clearly, Stack Overflow does not interpret the caret as a superscript instruction. However, the text is comprehensible, and this is what really matters when using Markdown.
<sup> and <sub> tags work and are your only good solution for arbitrary text. Other solutions include:
Unicode
If the superscript (or subscript) you need is of a mathematical nature, Unicode may well have you covered.
I've compiled a list of all the Unicode super and subscript characters I could identify in this gist. Some of the more common/useful ones are:
° SUPERSCRIPT ZERO (U+2070)¹ SUPERSCRIPT ONE (U+00B9)² SUPERSCRIPT TWO (U+00B2)³ SUPERSCRIPT THREE (U+00B3)n SUPERSCRIPT LATIN SMALL LETTER N (U+207F)People also often reach for <sup> and <sub> tags in an attempt to render specific symbols like these:
™ TRADE MARK SIGN (U+2122)® REGISTERED SIGN (U+00AE)? SERVICE MARK (U+2120)Assuming your editor supports Unicode, you can copy and paste the characters above directly into your document.
Alternatively, you could use the hex values above in an HTML character escape. Eg, ² instead of ². This works with GitHub (and should work anywhere else your Markdown is rendered to HTML) but is less readable when presented as raw text/Markdown.
Images
If your requirements are especially unusual, you can always just inline an image. The GitHub supported syntax is:
You can use a full path (eg. starting with https:// or http://) but it's often easier to use a relative path, which will load the image from the repo, relative to the Markdown document.
If you happen to know LaTeX (or want to learn it) you could do just about any text manipulation imaginable and render it to an image. Sites like Quicklatex make this quite easy.
Source: Stackoverflow.com