The statement that is 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 did influence various aspects of governance and trade, the assertion that it specifically helped in building powerful armies for expansion to the North and West is less accurate compared to the other statements, which more directly address cultural, architectural, and economic influences of Islam on these empires.