How many years after the death of mohamed did it take for the muslim empire to reach its fullest extant?

We see after the demise of Prophet Mohammad (PBUH) in 632, The Muslim empire reached to its fullest extent in 711 with the conquest of Spain.

So almost 79 years after the demise of Prophet Mohammad (PBUH),the Muslim empire reached to its fullest extent.It stretched from Spain to the borders of modern day China.

the answer to your question is:

strong-mayor system

b)

it created free trade throughout the colonial territories.