How did Islam trade help conquer a huge empire?

Answer 1

This question makes an incorrect implicit assumption, that the trade engaged in by Islamic Empires helped lead to conquest. The trade and conquest operated separately and in parallel, but had minimal crossover.

This question confuses the fact that Islam as a religion spread through both conquest (which created an apartheid power-dynamic incentivizing conversion) and through trade (which allowed Non-Muslims to meet Muslims and be awe-inspired by their religion), with Islam in its political dimension. The conquests were purely a component of Islam in politics.

The only way that trade could help in conquest is that trade resulted in better military equipment, either through trade in military equipment or through financial gains from trade being spent on local military equipment. However, the Islamic Imperial Economic System relied much more on booty (stolen wealth from conquered or savaged nations) and high taxes on Non-Muslims (jizya and inequitable kharaj taxes). Muslim armies only really began to import weapons from the west long after they were in decline, such as Morocco in the 16th century or the Ottoman Empire in the 18th century, so the huge empire is not really in play here.