Final answer:
Octavian won a decisive victory over Antony and Cleopatra in the Battle of Actium. The correct option is a.
Step-by-step explanation:
The decisive battle in which Octavian won a victory over Antony and Cleopatra is the Battle of Actium. The Battle of Actium took place in 31 BCE and was a naval battle between the forces of Octavian and Marcus Agrippa against Antony and Cleopatra. Octavian's forces emerged victorious, leading to the downfall of Antony and Cleopatra and the end of the Ptolemaic dynasty in Egypt.
This battle marked the start of Roman rule in Egypt and solidified Octavian's position as the undisputed master of the Roman world.
The correct option is a.