What destroyed African empires and cultural achievements starting in the 1400's and continuing until the 1800's

It is hard to give only one cause to such a big historical event. The decay of empires can be a long duration event with a dozen of causes. However in this case it is safe to say that this set of events has one common fundamental cause: transatlantic slave trade.

Explanation:

The transatlantic slave trade was a long duration event that completely changed internal dynamics of African empires. Although to say that it destroyed Africa's cultural achievements is too much, it certainly impacted the entire continent.

Africa had internal slave trade since long time before the 14th century. This trade however was small and connected with demands internal to states in the continent. When the atlantic trade started and became routine it was big business, the bigger of the modern era: it was a world trade that was responsible for much of the growing of many entire nations.

The last country to abolish slavery was Brazil in 1888. Transatlantic slave trade started in the 1400s with technological developments that improved navegation and ended in mid 1800s.