I understand that the order of operations is done as PEMDAS because exponentation is just repeated multiplication and multiplication is just repeated addition and you could even make division and subtraction into multiplication and addition respectively and consequently you could really write everything in terms of addition WHEN YOU'RE DEALING WITH NATURAL NUMBERS.

e.g. 2+3*4^2

= 2+3*(4*4)

= 2 + 3*(4+4+4+4)

= 2 + (4+4+4+4) + (4+4+4+4)+ (4+4+4+4)

but what's the explanation for why we still use PEMDAS for rational numbers?