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 empire build powerful armies and extend their power to the north and west."
While Islam did contribute to various aspects of society and governance in these empires, the statement about building powerful armies and territorial expansion is not a direct influence of Islam itself but rather a characteristic of empire-building that may occur for various political or economic reasons. The other statements more directly address the cultural and intellectual influences of Islam.