\begin{definition}[Definition:Power (Algebra)/Integer]
Let $x \in \R$ be a real number.
Let $n \in \Z$ be an integer.
The expression $x^n$ is called '''$x$ to the power of $n$'''.
$x^n$ is defined recursively as:
:$x^n = \begin{cases}
1 & : n = 0 \\
& \\
x \times x^{n - 1} & : n > 0 \\
& \\
\dfrac {x^{n + 1} } x & : n < 0
\end{cases}$
where $\dfrac{x^{n + 1} } x$ denotes quotient.
{{mistake|the quotient as linked is not actually the quotient of integers, because for $n < -1$ we have that $x^{n + 1}$ is not generally an integer.}}
\end{definition}