Category:Integer Powers

This category contains results about Integer Powers.
Definitions specific to this category can be found in Definitions/Integer Powers.

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 division.