The use of superscripts has been shown in each case of this content. Exponentiation is formed by the combination of **base** and **exponent or power**.

(**base**)^{(exp)} like** x ^{n}**,

**a**.

^{k}Power or exponent will always be defined by superscript, for which latex has `base^{exponent}`

syntax.

```
\documentclass{article}
\begin{document}
\[ (Base)^{exponent} \]
\[ x^n,K^n,p^q \]
\[ e^{\ln(x)} \]
\end{document}
```

**Output : **

If the length of the exponent or power is more than a single character, the whole exponent must pass through the curly bracket.

```
\documentclass{article}
\begin{document}
\[ x^pq \quad x^{pq} \]
\[ c^nk \quad c^{nk} \]
\[ x^a\ln (x) \quad x^{a\ln (x)} \]
\end{document}
```

**Output : **

## Exponential functions in LaTeX

Exponential functions are written in two ways. The first uses the base as **e** and the second uses the exponent as an argument in the exp function.

In latex, There is a pre-defined command for exp function.

```
\documentclass{article}
\begin{document}
\[ e^x \quad \exp(x) \]
\[ e^{\ln(x)} \quad \exp(\ln x) \]
\[ e^{n^2} \quad \exp(n^2) \]
\[ e^{1/x} \quad \exp(1/x) \]
\[ e^{\ln x/x} \quad \exp^{\ln x/x} \]
\[ (e^z)^n \quad \exp(nz) \]
\end{document}
```

**Output : **

## e^{pow} and exp(pow) which is best?

Have you ever wondered why this exponential function is defined in two ways? The main reason for this **is to maintain the beauty of mathematical expression.**

Below are some examples that will help you differentiate between the two cases.

And you can easily understand **what is right and what is wrong.**

```
\documentclass{article}
\begin{document}
\[ e^{(\frac{x}{x+1})} \quad \exp\left(\frac{x}{x+1}\right) \]
\[ e^{\ln x +k} \quad \exp(\ln x + k) \]
\[ e^{(\frac{\sin x}{x})} \quad \exp\left(\frac{\sin x}{x}\right) \]
\[ e^{\ln x^{\ln x}} \exp\left(\ln x^{\ln x}\right) \]
\end{document}
```

**Output : **

## Use continuous fractions for e^{x}

You may have noticed that the exponential function is written with the help of continuous fraction.

But in this case, `\cfrac{num}{den}`

best practice instead of `\frac{num}{den}`

command.

```
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[ e^x = 1+\cfrac{x}{1-\cfrac{x}{x+2 -\cfrac{2x}{x+3-\cfrac{3x}{x+4-\cfrac{4x}{\ddots}}}}} \]
\[ e^z = 1+\cfrac{2z}{2-z+\cfrac{z^2}{6 +\cfrac{z^2}{10+\cfrac{z^2}{14+\cfrac{z^2}{\ddots}}}}} \]
\end{document}
```

**Output : **