Question: Since the argument becomes too small when using `\frac`, is there an alternative way to reduce the size of the `\exp` argument?

```
    \documentclass{article}
    \usepackage[T1]{fontenc}
    \usepackage{lmodern}
    \usepackage{amsmath,amssymb,amsfonts,systeme} 
    \begin{document}

    $$\eta = A \exp^{-\dfrac{E_a}{RT}}$$

    \end{document}

```

[![enter image description here](https://i.stack.imgur.com/iPX65.png)](https://i.stack.imgur.com/iPX65.png)

Answer: 
You asked,

> 
> is there an alternative way to reduce the size of the `\exp` argument?
> 
> 
> 

If one uses `\exp` notation, one should *not* raise the argument to superscript height. Instead, simply encase the argument in round parentheses, square brackets, or whatever fence symbols are most suitable to the task.

Separately, to avoid having to display fractional expression in superscript position, do consider using so-called inline-fraction notation. E.g., instead of writing `e^{\frac{u}{v}}`, write `e^{u/v}` -- or `\exp(u/v)`.

[![enter image description here](https://i.stack.imgur.com/jjN7r.png)](https://i.stack.imgur.com/jjN7r.png)

```
\documentclass{article}
\begin{document}
\[
\eta = e^{-E_a/RT} = A \exp(-E_a/RT)
\]
\end{document}

```
First, don't use `$$ .. $$` for displayed math, use `\[ .. \]` instead. Second, you can make the fraction in the exponent larder than `\frac` in two ways; either expand `-E_a/RT` or use normal size of `\frac` by any of several methods, I here used `\mbox`. `\tfrac` will also do the same but is easier. 

```
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{amsmath,amssymb,amsfonts,systeme} 
\begin{document}

\begin{align*}
\eta &= A \exp^{-E_a/RT} \\
\eta &= A \exp^{\mbox{$-\frac{E_a}{RT}$}} \\
\eta &= A \exp^{-\tfrac{E_a}{RT}} \\
\eta &= A \exp^{-\frac{E_a}{RT}}
\end{align*} 

\end{document}

```

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> [![enter image description here](https://i.stack.imgur.com/d9cGf.png)](https://i.stack.imgur.com/d9cGf.png)
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