Is the P E M/D A/S convention necessary to be compatible with exponent notation?

If we write: $\displaystyle 2^3 + 7 $

then wouldn't it be impossible to reverse the priority of exponents and addition if we use our current notation for exponents?

- Mar 20th 2011, 09:56 PMlamp23Is the PEMDAS convention necessary to be compatible with exponent notation?
Is the P E M/D A/S convention necessary to be compatible with exponent notation?

If we write: $\displaystyle 2^3 + 7 $

then wouldn't it be impossible to reverse the priority of exponents and addition if we use our current notation for exponents? - Mar 20th 2011, 10:51 PMProve It
I don't understand your question - it's very clear that you need to do the exponentiation before the addition...

- Mar 20th 2011, 11:14 PMlamp23
I'm asking if the order of operations convention that we adopt, namely P E M/D A/S, could have been a different convention. It seems possible that we could have adopted a convention of P E A/S M/D i.e. reversing the priority of addition and multiplication so that $\displaystyle 4 \times 2+1 = 4 \times 3$.

However, I don't see how we could do something similar with exponents. - Mar 21st 2011, 01:06 AMemakarovQuote:

Is the P E M/D A/S convention necessary to be compatible with exponent notation?

*necessary*because you can make a convention to do M/D after A/S. However, our notation for exponents does seem to imply that exponentiation has the highest priority.