exponent
/ĭk-spō′nənt, ĕk′spō″nənt/
noun
- One that expounds or interprets.
- One that speaks for, represents, or advocates. Our senator is an exponent of free trade.
- (Mathematics) A number or symbol, as 3 in (x + y)3, placed to the right of and above another number, symbol, or expression, denoting the power to which that number, symbol, or expression is to be raised.
Since the Oxford English Dictionary is behind a paywall, I can't blame you for not surfacing this:
exponentiate, v.
Mathematics.
1. intransitive. To increase exponentially; also, more generally, to exhibit specified asymptotic behaviour as some limit is approached.
2. transitive. To raise e or some other base (BASE n.1 20) to the power of; to subject to exponentiation. Also absol.
Source: Oxford English Dictionary (login required)
Here are a couple of usage examples supplied . . .
Intransitive:
1971 Physical Rev. D. 3 970 We find that the leading Regge-pole term arising from single-ladder-exchange exponentiates.
Transitive:
1978 Physics Lett. A. 64 477/2 By solving the operator equations in their full nonlinear form..we are able to exponentiate the logarithmic terms into power law singularities.
Go forth and exponentiate.
Answer from Tinfoil Hat on Stack ExchangeTwo alternatives with automatically resized N:
\documentclass{article}
\usepackage{amstext}% or package amsmath for \text
\newcommand*{\ttmath}[1]{%
\texttt{\mdseries\upshape#1}%
}
\begin{document}
$2^{\verb|N|-1}$ {\small(\verb|\verb|)}
$2^{\texttt{N}-1}$ {\small(\verb|\texttt| with \verb|amstext|)}
\textit{Italics $2^{\ttmath{N}-1}$ context} {\small(macro \verb|\ttmath|)}
$2^{\mathtt{N}-1}$ {\small(\verb|\mathtt|)}
\end{document}
Remarks:
\texttthere works with automatically resizing in math mode because it internally uses\nfss@textthat is redefined in packageamstextas\text.Macro
\ttmathalso resets font attributes series and shape to get independent from the current text font setting.\mathttis the most efficient command and uses the configured typewriter font for math. This is often the same as\ttfamily. Some font packages switch both fonts at the same time aslmodern, others do not asberamono. Therefore, it depends on the font setup, whether\mathttcan be used instead of\verbor\texttt.
The LaTeX kernel defines \mathtt and nothing else is necessary. By the way, \verb should not be abused for printing in the typewriter font, usually \texttt is enough, whereas \verb is needed for printing TeX code with special characters.
\documentclass{article}
\begin{document}
$2^{\mathtt{N}-1}$
$2^{\mathtt{N}^{\mathtt{M}}}$
\end{document}

It's probably useful to define your own semantic command, say
\newcommand{\tvar}[1]{\mathtt{#1}}
and use $2^{\tvar{N}}$. This way you're not tied to the particular representation that you can change at any time by just modifying the definition.
It may happen that the choice of a different font set doesn't update \mathtt. The solution is simple and the advantage over other solutions involving \text is that this can be easily adapted to support \boldmath out of the box.
\documentclass{article}
\usepackage[T1]{fontenc} % necessary for beramono
\usepackage{amsmath}
\usepackage{beramono}
% update \mathtt to use the same font as \ttfamily
\DeclareMathAlphabet{\mathtt}{\encodingdefault}{\ttdefault}{m}{n}
% if the monospaced font also supports boldface (b or bx)
\SetMathAlphabet{\mathtt}{\encodingdefault}{\ttdefault}{b}{n}
\newtheorem{theorem}{Theorem}
\begin{document}
$2^{\mathtt{N}-1}$ and \texttt{N}
\begin{theorem}
Something about $2^{\mathtt{N}-1}$
\end{theorem}
\end{document}

Side note
Using \texttt is wrong, as exemplified by the following code.
\documentclass{article}
\usepackage{amsmath}
\newcommand{\tvar}[1]{\mathtt{#1}}
\newtheorem{theorem}{Theorem}
\begin{document}
\section*{Right}
$2^{\tvar{N}-1}$
\begin{theorem}
Something about $2^{\tvar{N}-1}$
\end{theorem}
\section*{Wrong}
$2^{\texttt{N}-1}$
\begin{theorem}
Something about $2^{\texttt{N}-1}$
\end{theorem}
\end{document}

Ex)
y=ln|x| --> x=ey
What the heck did I just do? "e" both sides? "Eulerize" both sides? Is there even a word for it?
Edit: "Exponentiate" seems to be the popular answer! However, a quick Google search of the term to double check describes it as (and correct me if I'm wrong) raising a base to an exponent. But in whatever I did above, I didn't raise both sides to a power; I raised "e" to the power of each side right? So idk... "exponentiate e by each side" might be what I say until someone says otherwise.
Edit 2: I might try to start "Eulerentiation" lol
