Final answer:
The Roman Empire was at its strongest from 27 BC to 180 AD, a period known as the Pax Romana, which was marked by peace, prosperity, and expansion.
Step-by-step explanation:
The height of the Roman Empire, at its strongest, is widely considered to have been from 27 BC to 180 AD, a period known as the Pax Romana. During this time, the Empire expanded significantly under the leadership of Emperor Augustus Caesar and subsequent rulers, stretching across three continents and boasting great achievements in engineering and architecture. This era provided not just a powerful military presence but also a time of peace and prosperity internally, allowing for extensive trade and communication throughout the vast territory. The answer to the student's question is A) 27 BC to 180 AD.