If wizards are so powerful then why do they hide from muggles?
well that's the weird part in an of itself...the explanation for the statute was a combination of persecution and distrust yet there is nothing to suggest witches and wizards actually fought back against muggles leading up to the new law. the way it reads the wizarding community seemed to have taken a pacifistic stance to any conflict with muggles and as a result just as many were killed as those that escaped.
this would seem to suggest that muggles would win in a war because clearly wizards withdrew from the world because of persecution. yet the way the decision has been explained it seems that wizards didn't even try to fight muggles at this point. more like they became disgusted and broke off from those they once considered neighbors and friends.
this was also a similar period when magical schools were beginning to form and thus could open up another question.....are wizards today more powerful than they were (as a collective) at the time they began hiding? certainly there were individual great witches and wizards and Ron stated Egyptian wizards knew extremely powerful curses but as a whole was the wizarding community weaker then then now because their knowledge wasn't solidified and taught to each generation as a whole whereas before knowledge and spells were probably handed down within families. so the number of spells a single wizard may know today could be far greater than was known then because the wizarding community wasn't a united body as it became following the statute.
basically muggles had better odds against wizards in the past because they were isolated from one another. easier to pick-up a small family than an entire village.
that doesn't apply as much anymore as wizards have spent centuries as a collective, sharing knowledge and growing together, though there is still a division of geography as they have different Ministry for Magics, which only makes sense given the number of countries and backgrounds the wizarding community covers living alongside their muggle counterparts.