The statement that was NOT one of the many ways that Islam influenced the achievements of the Mali and Songhai empires is:
Islam helped both the Mali and Songhai empires build powerful armies and extend their power to the North and West.
While Islam may have contributed to the cohesion and organization of armies, the primary achievements of these empires in terms of military power were more significantly influenced by other factors such as leadership, resources, and pre-existing military strategies, rather than a direct influence of Islam in this specific context. The other choices focus on the cultural, architectural, and economic impacts of Islam, which were more integral to the achievements of these empires.