why in algebra class they teach the order of operations (PEMDAS) in that order. Is this just an arbitrary standard everyone agreed on or was it the result of higher math only making sense when equations are done in that order?

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I see a lot of folks saying it’s arbitrary, It’s just math and it doesn’t matter how we do it as long as we all do it the same. That is not correct. Math represents real life. You do pemdas because following this rule guarantees you will get real life results. Here’s the best example I’ve seen in the past (for this example forgive the strange farm that has octopus’ and consider their tentacles legs):
You go to a farm and there are 5 chickens, 3 cows and 2 octopuses. How many legs are there? Well if you count the legs you get 38. If you use math:
5×2+3×4+2×8 = 10+12+16 = 38 legs. This is why you must do multiplication first. It’s not arbitrary. Now the way we write this (symbols of + x etc and use of parenthesis, sure that’s arbitrary) but order of operations is required to have math match real life. There’s still confusion around other elements of pemdas, and memorizing rules is a terrible way to “understand” things. but the bottom line is, it’s not arbitrary. Source: I’m an engineer. Edited for clarity