Which intervention most contributed to the spread of both the ottoman and the safavid empires

Gunpowder

The correct answer is gunpowder.

The Ottoman Empire introduced firearms in its military troops in the late 14th century and beginning of the 15th century. Later, this artillery troops professionalized and specialized into different groups: the Piyade Topçu (foot artillery), Süvari Topçu (mounted artillery), and humbaraci (bombardiers and mortar troops), which helped them expand and keep their frontiers.

The Safavid Empire under the rule of Shah Abbas (1571-1629), as Ottomans did before, started a series of reforms of the army which involved the introduction of firearms. Tofang-chis (musketeers), artillery corps were added to the traditional armies and cannons provided by European powers.