I've struggled to find in google the exact definition of the word "orders" as used in bodmas's second operation. I know what it means (powers, indeces etc.) but I'm looking for the proper mathematical definition and how I could use it in a sentence. Can I say for example "3 raised to the order 2"?
Edit to add: I'm referring to the "orders" in the mnemonic as in brackets, orders, division etc. where orders means powers. Not about order in "order of operations".
On
"BODMAS" may well be taught before students have even encountered the notion of exponentiation. In that context it really should be "BDMAS"*, but of course this is not readily pronounceable so an "O" was added. The explanation I was given at school was that this stood for "of" (i.e. the other things can be inside the brackets), which doesn't really mean anything. I suspect "order" was just a post-hoc attempt to make this include exponentiation without changing the acronym; it's not used with that meaning elsewhere in mathematics.
*or really "$\mathrm{B}^\mbox{D}_\mbox{M}{}^\mbox{A}_\mbox{S}$" since D/M (mostly) have equal precedence, as do A/S, but that's even harder to say.
There is no mathematical definition of orders. It's used here as a collective lay term and not as a proper mathematical one.