Native Americans in South America weren’t exterminated during those days. You can see them today, mostly mixed with the European race. But it’s true Columbus treated natives as inferior and even took some of them slaves. Much later, some south American countries, like Argentina or Chile did indeed exterminate the indigenous population after they gained their independence from Spain. While many natives died of diseases brought by Europeans, under Spanish rule, natives were king’s subjects and there were laws to protect them (violated frequently, though). However, this is unlike North America, where natives were mostly exterminated.