I don't understand your question - it's very clear that you need to do the exponentiation before the addition...
Is the P E M/D A/S convention necessary to be compatible with exponent notation?
If we write:
then wouldn't it be impossible to reverse the priority of exponents and addition if we use our current notation for exponents?
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 .
However, I don't see how we could do something similar with exponents.
It is not 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.Is the P E M/D A/S convention necessary to be compatible with exponent notation?