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Hey, Vsauce, Michael here!
What would a real life act of exterminatus look like, and is such a thing even scientifically feasible? Well… it turns out that it's actually a lot easier than you might think!
Now, I know a lot of you are already thinking about nuclear weapons, but those come with a lot of nasty issues. We'll discard the idea of using nuclear weapons, seeing how we want to resettle and extract resources from the land, which would of course be complicated by contamination with radionuclides. Instead, let us imagine a purely hypothetical carpet bombardment of the Indian subcontinent with nerve agents.
VX is the most potent and easily weaponized, so let us start by asking how many tons of munitions containing VX it'd take to rid South Asia of its current inhabitants. Doing the math, approximately 1.500 liters of VX would be enough to deal with the entire population of India, but that's of course assuming an ideal distribution and no loss of the agent due to environmental conditions. We need to keep in mind that the degradation of VX is accelerated by high temperatures and water. For maximum effectiveness, the munitions would have to be deployed during the Indian dry season where it's both the driest and coolest time of the year, so that any degradation of the agent due to humidity and heat is minimized. We also need to take the populations of Bangladesh and Pakistan into account, which would require an additional 4-to-500 liters of VX. An American M55 rocket can carry 4 liters of the VX agent, so we would need 500+ rockets to get the job done, which is well within the production capacity of a major first world military power.
So yes, exterminatus of the Indian subcontinent is not only possible, it's actually fairly easy to achieve