Which operation should be performed first for calculations involving more than one arithmetic operation?
a)parentheses
b)exponents
c)multiplication division

The answer is:  [A]:  parentheses .

The mnemonic to remember is: 

PE  MD AS ; or:

BE  MD AS


Please excuse my dear Aunt Sally/Susan. ; or:

Be excused, my dear Aunt Sally/Susan.


which means, start with Parentheses (or BRACKETS);  
 THEN do exponents;
Then "multiplication division" (from left to right as they appear);
Then "addition subtraction" (from left to right, as they appear).

The three (3) answer choices given are:

   a) parentheses ;
   b) exponents;
   c) multiplication division.

We know from our mnemonic that BOTH parentheses AND exponents (i.e. choices "A" and "B" come before "Multiplication and Division" (answer choice "C"); so we can rule out "answer choice C".  We are left with answer choices: a) parentheses; and:  b) exponents.  We know from our mnemonic that parentheses come before exponents, so, we rule out "answer choice B", and we know that "answer choice: {A}: parentheses" — is the correct answer.