I have a test where I am given the following article, what is an answer for the question: What are the full names of the two dynasties that were followed by imperial Kannada empires such as the Badami Chalukyas, the Rashtrakuta Empire of Manyakheta and the Western Chalukya Empire? ?

Karnataka's pre-history goes back to a paleolithic hand-axe culture evidenced by discoveries of, among other things, hand axes and cleavers in the region. Evidence of neolithic and megalithic cultures have also been found in the state. Gold discovered in Harappa was found to be imported from mines in Karnataka, prompting scholars to hypothesise about contacts between ancient Karnataka and the Indus Valley Civilisation ca. 3300 BCE.Prior to the third century BCE, most of Karnataka formed part of the Nanda Empire before coming under the Mauryan empire of Emperor Ashoka. Four centuries of Satavahana rule followed, allowing them to control large areas of Karnataka. The decline of Satavahana power led to the rise of the earliest native kingdoms, the Kadambas and the Western Gangas, marking the region's emergence as an independent political entity. The Kadamba Dynasty, founded by Mayurasharma, had its capital at Banavasi; the Western Ganga Dynasty was formed with Talakad as its capital.
These were also the first kingdoms to use Kannada in administration, as evidenced by the Halmidi inscription and a fifth-century copper coin discovered at Banavasi. These dynasties were followed by imperial Kannada empires such as the Badami Chalukyas, the Rashtrakuta Empire of Manyakheta and the Western Chalukya Empire, which ruled over large parts of the Deccan and had their capitals in what is now Karnataka. The Western Chalukyas patronised a unique style of architecture and Kannada literature which became a precursor to the Hoysala art of the 12th century. Parts of modern-day Southern Karnataka (Gangavadi) were occupied by the Chola Empire at the turn of the 11th century. The Cholas and the Hoysalas fought over the region in the early 12th century before it eventually came under Hoysala rule.

Kadamba Dynasty