How power is extended vertically through hierarchies and horizontally through industrial networks and markets is a classic issue in sociology that was once extensively studied by Weber. Yet it is little studied today. Definitions of power exclude power exercise beyond the single relation, as does research in exchange networks. In contrast, research in organizations recognizes the extension of power, but offers no theory to explain how it is produced or to identify the conditions which might further or impede it. Here the extension of power beyond the single relationship is called power-at-a-distance. New theory offering metric predictions is applied to power-ata- distance in exchange networks. That theory identifies the conditions that extend power beyond the dyad and the conditions that tend to block that extension. Five experiments on contrasting structures broadly support those predictions. Relations between power-at-a-distance and power centralization are theorized. Practical problems of extending power are addressed and further research is proposed.