Option 1 -> The 6th century CE marks the rise of the Chalukyas of Badami (founded ~543 CE by Pulakeshin I) and the Pallavas' emergence as a major power in Tamil Nadu.
Option 2 -> 500-600 BCE is too early; this predates both dynasties by nearly a millennium when the region had different political formations.
Option 3 -> 100-200 CE is the early historical period when these dynasties had not yet emerged as major powers in their respective regions.
Option 4 -> 100-200 BCE falls in the late prehistoric/early historical period, well before either dynasty's formation.
Hence, Option 1: 500-600 CE -> Both the Chalukyas in Karnataka and the Pallavas in Tamil Nadu rose to prominence during the 6th century CE, establishing powerful kingdoms that would dominate South Indian politics and culture for centuries -> correct