Definition:Power (Algebra)/Multiindices

Definition

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:

$\ds x^k := \prod_{j \mathop = 1}^n x_j^{k_j}$

where the powers on the right hand side are integer powers.