Using Scholze-Weinstein description of the Rapoport-Zink spaces in terms of p-adic Hodge theory and the vector bundles on the Fargues-Fontaine curve, we show that a certain diagram constructed via the exterior power morphism from the Lubin-Tate tower to the Rapoport-Zink tower is Cartesian. The special case of the determinant morphism is a theorem of Scholze-Weinstein. This result helps us understand the behavior of the exterior power morphism via-à-vis the period morphisms on the Lubin-Tate and Rapoport-Zink towers.