How did the battles at Marathon and Thermopylae lead to the downfall of the Persian Empire?

Answer 1

At Marathon a Persian punitive expedition against Eretria and Athens was turned back by a combined army of Athens and its ally Plataia. It demonstrated to the rest of the Greek cities that the Persians could be resisted successfully, and also the superiority of armoured infantry over unarmoured infantry which was not supported by cavalry. This lesson was utilised ten years later by the combined Greek city armies at Plataia where the Greeks kept to rough country to neutralise the Persian cavalry and defeated the Persian infantry.

The battle of Thermopylai was a brief delaying action during the later Persian invasion, and achieved no result at all, but became a Propaganda tool used to inspire the Greeks.

After 50 years of attempting to impose peace on the Greeks, the Persians gave up and left the Greek cities to their usual destructive fighting amongst each other, and concentrated on running their Empire.

So the two battles had nothing to do with the downfall of the Persian Empire. In fact a century later the Persians, tired of this Greek infighting spilling over and disrupting their Empire, imposed the King's Peace, threatening reprisal on the Greek cities if they continued their endless warring on each other.

The downfall of the Persian Empire was accomplished by Macedonia when Alexander the Great captured it in 331 BCE, a hundred and fifty years after Marathon (490 BCE) and Thermopylai (480 BCE).

The statement in the question is the equivalent of saying 'how did Napoleon's defeat of Prussia in 1806 lead to the downfall of Nazi Germany in 1945'.