'power-intensive' is a compound formed from the noun 'power' (from Old French 'pouvoir', via Middle English, ultimately with Latin roots related to ability/force) and the adjective 'intensive' (from Latin 'intensivus'/'intensus', via French and Late Latin), where 'intensive' carried the sense of 'applied strongly or to a high degree'.

'power' came into English via Middle English from Old French 'pouvoir' (itself from Latin-rooted forms conveying ability/force), becoming the general noun 'power' in modern English; 'intensive' descended from Latin 'intensus'/'intensivus', passed into French as 'intensif' and into English as 'intensive', and the two were later combined in modern technical usage to form 'power-intensive'.

Initially, 'power' emphasized ability or force and 'intensive' meant 'stretched inward' or 'applied with force'; over time 'intensive' evolved to mean 'to a high degree' or 'demanding much of a resource', so the compound came to mean 'requiring a large amount of power'.