Let $X_1, \ldots, X_N$ each be a D17: Finite set such that

(i) | $K_1, \ldots, K_N \in \mathbb{N}$ are each a D996: Natural number |

(ii) | \begin{equation} |X_1| = K_1, \quad \ldots, \quad |X_N| = K_N \end{equation} |

(iii) | $X : = \prod_{n = 1}^N X_n$ is the D326: Cartesian product of $X_1, \dots, X_N$ |

(iv) | $\mathcal{R} : = \{ R : R \subseteq X \}$ is a D5494: Set of N-ary relations on $X$ |

Then
\begin{equation}
|\mathcal{R}| = 2^{\prod_{n = 1}^N K_n}
\end{equation}