Submitted by **TheManNamedPeterPan** t3_z8c5vf
in **explainlikeimfive**

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**MoobooMagoo**
t1_iyc0zud wrote

Reply to comment by **DecentChanceOfLousy** in **ELI5 why we first multiply, then add** by **TheManNamedPeterPan**

You're not wrong, but most of the confusion with order of operations happens at the multiplication -> addition level. At least in my experience. Like 5x^2 is really obvious what it's supposed to be to most people (if you're using actual super script, anyway).

Although that said, I understand that this very well may be because once you start doing more complicated math that actually requires a lot of parentheses and exponents and stuff you've already used the order of operations so many times it starts to become second nature, so it might just be that those are more obvious because the people that are encountering them are already well practiced.

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**SirX86**
t1_iyc20rc wrote

>Like 5x^2 is really obvious what it's supposed to be to most people

In the spirit of the original question, you could argue: why is it obvious that 5x² means 5*(x²) and not (5*x)²?

Indeed people often get confused over -x²: is that (-1)*(x²) or (-1*x)²?

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**SupaFugDup**
t1_iyc6y57 wrote

Just to be sure, it is -1(x²) right?

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**-Revelation-**
t1_iyc9brh wrote

it is

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**Kalirren**
t1_iycayo7 wrote

And the answer to the "why" is because exponentiation distributes over multiplication, and not the other way around, just like multiplication distributes over addition.

xy^(2) = x*(y^2) = x*y^2 != (x*y)^2 = (xy)^(2) = x^(2)y^(2)

x*(y^2) != (x*y) ^ (x*2)

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**No-Eggplant-5396**
t1_iyed1g0 wrote

Convention. It's like the alphabet. The alphabet isn't required to be in ABC ordering by a fundamental force of nature but rather just some particular ordering for better communication.

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**DecentChanceOfLousy**
t1_iyc1nqo wrote

That is, indeed, the whole point. You practice them so that they become second nature when you do more complicated math.

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