Question

How did the Pax Romana allow Rome to flourish,grow, and remain relatively stable and peaceful

Answer 1

Under the period of the Pax Romana, Rome allowed the provinces--the places they had conquered--to make their own laws and govern many of their own affairs.  The conquered lands accepted Roman taxation and Roman military presence, guarding the peace and stability of each area.  This was the strategy that allowed the Roman Empire to flourish and enjoy much stability during the "Roman Peace" (Pax Romana) era.

The Pax Romana is noted as a time within the Roman Empire that lasted for around 300 years, rom the reign of Caesar Augustus (27 BC – AD 14) until the reign of Marcus Aurelius (AD 161 –180 CE).