Priority of operations

Question

I got confused by this simple question and need clarification

The last digit of 6^4/2

Is it:

Last digit of 6^4 / 2 = 6/2 = 3

Or:

Last digit of 6*(6^3)/2 = 3*(6^3) = 3*6 = 8

Which is correct ?

Bunuel · Answer

The second approach is correct. Check similar question here: what-is-the-last-digit-of-88453.html

Lucky2783 · Answer

snippet from  Bunuel  's Mathbook .

ORDER OF OPERATIONS - PEMDAS

Perform the operations inside a  P arenthesis first (absolute value signs also fall into this category), then  E xponents, then  M ultiplication and  D ivision, from left to right, then  A ddition and  S ubtraction, from left to right - PEMDAS.

Special cases:
• An exclamation mark indicates that one should compute the factorial of the term immediately to its left, before computing any of the lower-precedence operations, unless grouping symbols dictate otherwise. But  3^2!  means  (3^2)! = 9!  while  2^{5!} = 2^{120} ; a factorial in an exponent applies to the exponent, while a factorial not in the exponent applies to the entire power.

• If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
 a^m^n=a^{(m^n)}  and not  (a^m)^n

Priority of operations

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