Synopsis (in math mode or display math mode), one of:

base^expbase^{exp}

or, one of:

base_expbase_{exp}

Make `exp` appear as a superscript of `base` (with the caret
character, `^`

) or a subscript (with
underscore, `_`

).

In this example the `0`

’s and `1`

’s are subscripts while the
`2`

’s are superscripts.

\( (x_0+x_1)^2 \leq (x_0)^2+(x_1)^2 \)

To have the subscript or superscript contain more than one character,
surround the expression with curly braces, as in `e^{-2x}`

.
This example’s fourth line shows curly braces used to group an expression
for the exponent.

\begin{displaymath} (3^3)^3=27^3=19\,683 \qquad 3^{(3^3)}=3^{27}=7\,625\,597\,484\,987 \end{displaymath}

LaTeX knows how to handle a superscript on a superscript, or a
subscript on a subscript, or supers on subs, or subs on supers. So,
expressions such as `e^{x^2}`

and `x_{i_0}`

give correct
output. Note the use in those expressions of curly braces to give the
`base` a determined `exp`. If you enter `\(3^3^3\)`

, this
interpreted as `\(3^{3}^{3}\)`

and then you get TeX error
‘`Double superscript`’.

LaTeX does the right thing when something has both a subscript and a superscript. In this example the integral has both. They come out in the correct place without any author intervention.

\begin{displaymath} \int_{x=a}^b f'(x)\,dx = f(b)-f(a) \end{displaymath}

Note the curly braces around `x=a`

to make the entire expression a
subscript.

To put a superscript or subscript before a symbol, use a construct like
`{}_t K^2`

. The empty curly braces `{}`

give the
subscript something to attach to and keeps it from accidentally
attaching to a prior symbols.

Using the subscript or superscript character outside of math mode or
display math mode, as in `the expression x^2`

, will get you
the TeX error ‘`Missing $ inserted`’.

A common reason to want subscripts outside of a mathematics mode is to
typeset chemical formulas. There are packages for that, such as
`mhchem`

; see CTAN.