Final answer:
The Hellenistic Age followed the Classical Age, marked by the expansion of Greek culture after Alexander the Great's conquests and the subsequent division of his empire.
Step-by-step explanation:
The era that succeeded the Classical Age and is characterized by the spread of Greek culture under the influence of Alexander the Great is known as the Hellenistic Age. This period followed Alexander's conquests, which saw Greek civilization extend throughout the entire Middle East. After his death, his empire was divided among his top generals, leading to a new cultural synthesis that was neither purely Greek nor non-Greek, but a blend that we refer to as Hellenistic.