You always solve parentheses first before solving for exponents, multiplication/division and addition/subtraction, but for the following problem 6/2(2+1), if solved division first then parentheses it still comes out to the same answer of 9... Is there a problem more definitive I can use to show that parentheses has to come first?

Question

anonymous · Answer

Actually solving parens doesn't really matter so long as you do solve them before you remove them. You can do them first or last it will still work properly.

anonymous · Answer

It absolutely does matter, especially in more advanced problems... Which is why the rule is there to begin with, but I was looking for a  simpler problem that takes the use of parentheses and has you apply the rule of order of operations instead of just being bypassed like you can in the equation given in my last text.

anonymous · Answer

I disagree. You don't need to solve the inside of an expression first. You only need to solve it before you take off the parens.

I can only really come up with 3 cases:

Addition/subtraction:
5 + (6-3)   Obviously fine
(-2+3) - 4  No issue here

Multiplication/division:
4/5(3+2)    Still doesn't matter
5/(3+2)7    Nope

Exponents:
4(4+2)^5
etc.


Can you come up with any example where evaluating the inside of the parens is required for correctness?