Is there a correlation between the size of an empire and the amount of power it holds in the world?

Yes.

Explanation:

The largest empires in the history of humankind have had a large mount of power over the world, for example the Mongol empire for a while reign over a large portion of Asia, and it had a lot of power over the world, the Roman empire had the same amount of power and influence over western and eastern Europe for over 10 centuries. The expansion of a empire is directly correlated to the power and influence it holds in the world.

Yes i'd say so, at least that's what history has taught us. The largest empires were the ones who are known today as being "world powers" because since a lot of land belonged to them they held most of the power. A great example of this is the Roman Empire