Using specific examples, explain how the Ottoman and Safavid Empires were able to control such extensive territory.

The Ottoman and Safavid Empires were able to maintain control over such an extensive territory through use of expansive bureaucracies, even though the forms of administration were drastically different from one another.  The Ottoman Empire, being more ethnically and religiously fractured than the Safavid, relied heavily on the millet system. Millets were the various religious communities of the empire, and to them was assigned much of the responsibility of administration. Marriages, criminal cases, and contracts were all handled by each individual millet, only relying on Ottoman authorities in those cases where issues were unresolved across denominational boundaries.
Meanwhile, the Safavid Empire drew on earlier Persian antecedents to establish a bureaucracy that was farther reaching in the lives of its subjects. However, this was balanced through the use of local rulers who in turn only had to pay a portion of their taxes to the central government.  As a result, local monies could be kept to better administer each individual area, or, less idealistically, kept by corrupt local officials willing to pay off any challengers.