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SirX86 t1_iyc20rc wrote

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

>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 (-1x)²?

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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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