Final answer:
The gunpowder technology, particularly firearms and artillery, played a crucial role in the growth and expansion of the Ottoman, Safavid, and Mughal Empires, earning them the historical term 'gunpowder empires'.
Step-by-step explanation:
The technology that facilitated the growth of the Ottoman, Safavid, and Mughal Empires was the military application of gunpowder, which includes firearms and artillery. These empires, often referred to as the 'gunpowder empires,' were able to effectively use and improve upon this technology to consolidate their power and expand their territories.
Significant to these empires' successes were the use of gunpowder arms, such as the arquebus and cannon, which provided them with a significant military advantage over their adversaries. This era of advancements in military technology also saw innovations like the use of trigonometry to calculate the qibla and the adoption of improved military strategies and tactics, contributing to their overall growth and stability.