Question 551053: Here is a problem:
2 2
(3) + (4) = (I believe the anwser is: (9) + (16) = 25
But there are time when only the exponents are added and not the whole
numbers. When do I know how to tell the difference in solving?
Found 2 solutions by mananth, KMST:
Answer by mananth(16946)   (Show Source):
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! Maybe you meant to ask a deeper philosophical question about why  means what the teacher says it means. There are meanings that are agreed upon by so many that you have to agree too, even if it sounds wrong to you. If most everyone says "grandma brought me a present," you cannot keep saying "grandma bringed me a present," or "grandma brang me a present."
In algebra, there are a few (very few) agreed upon rules and definitions that need to be agreed to and remembered. The rest of what you are told does not need to be memorized. Everything else in algebra can be derived from a handful of rules and definitions by using your own head, unlike your grandma'a phone number, which cannot be derived from anything else. Of course, having handy the quadratic formula, and/or the times tables, and/or grandma'a phone number is helpful. If you use them often enough and long enough, you'll remember them anyway, but only grandma'a phone number needs to be memorized.
Did you mean to ask why you have to calculate
 and  first, before adding them, when you are calculating
?
It's done that way, because of rules established long ago.
A long time ago, rules were established to make writing algebra sentences simpler, while still clear. Everyone agreed that expressions within parentheses (P) would be calculated first. Beyond that, it was decided that exponents (E) would take priority over everything else. After that, multiplication and division (as equal partners) were given priority over addition and subtraction (another pair of equal partners).
Teachers give students the acronym PEMDAS, or PE(MD)(AS) to help them remember.
Without those rules, writing math would require a lot of parentheses. To be understood the same way by all, the total cost of 6 packs of socks at $7 a pack, plus 2 underpants at $4 each, plus 3 T-shirts at $5 each would be written as
 instead of 
Even worse,
 would have to be written as
 .
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