Repeated multiplication of a variable with itself can also be written as a power:

$$\begin{array}{rcl} \blue{a}^\orange{n} & =& \underbrace{\blue{a} \cdot \blue{a} \cdot \ldots \cdot \blue{a}}_{\orange{n}\textrm{ times}} \end{array}$$

We call $\blue{a}^\orange{n}$ the $\orange{n}$-th power of $\blue{a}$.
The number $\blue{a}$ is called the base, and $\orange{n}$ is the exponent.

Next to that, we have $\blue{a}^\orange{0}=1$.

Examples

$$\begin{array}{rcl} \blue x^\orange0 &=& 1 \\ \blue x^\orange1 &=& \blue x \\ \blue{x}^\orange{2} & = &\blue{x} \cdot \blue{x} \\ \blue{x}^{\orange{3}} &=& \blue{x} \cdot \blue{x} \cdot \blue{x} \\ \blue{x}^\orange{4} &=& \blue{x} \cdot \blue{x} \cdot \blue{x} \cdot \blue{x} \end{array}$$

For integer $\orange n > 0$ and $\blue a \ne 0$ we define:

$$\blue{a}^{-\orange{n}}=\dfrac{1}{\blue{a}^\orange{n}}$$

Examples

$$\begin{array}{rcl}\blue{x}^{-\orange{1}}&=& \dfrac{1}{\blue{x}^\orange{1}} \\ \blue{x}^{-\orange{2}}&=& \dfrac{1}{\blue{x}^\orange{2}}\\ \blue{x}^{-\orange{3}}&=& \dfrac{1}{\blue{x}^\orange{3}} \end{array}$$