# Definition:Power (Algebra)/Multiindices

Let $k = \left \langle {k_j}\right \rangle_{j = 1, \ldots, n}$ be a multiindex indexed by $\set {1, \ldots, n}$.
Let $x = \tuple {x_1, \ldots, x_n} \in \R^n$ be an ordered tuple of real numbers.
Then $x^k$ is defined as:
$\ds x^k := \prod_{j \mathop = 1}^n x_j^{k_j}$