Question

Which egyptian king exerted his authority over the nubians through monumental structures such as his rock-cut temple at abu simbel?

Answer 1

We can approach this question by asking: who (ordered) built the Abu Simbel? The answer is Ramzes II, a pharaoh also known for reigning for 66 years, and whose reign is considered very good for Egypt ecomomically. 

And indeed, Ramzes also subjugated the Numbians, and it is suggested that he chose that place for his structures to reinforce the idea of himself as a strong leader. 

The answer is: Ramzes the Second!