Order of operations. Brackets (All Mathematical Formulae) --By: Vinod Kumar Dhundhara

Order of operations. Brackets

If  brackets are absent, the following order of operations is right:
    1)   raising to a power and extraction of a root (one after another);
    2)   multiplication and division (one after another);
    3)   addition and subtraction (one after another).
If  brackets are present,  at first all operations inside brackets are executedaccording to the aforesaid order, and then the rest of the operations out of brackets are executed (in the same order).

E x a m p l e . Calculate the next expression:

                                   ( 10 + 2³ · 3 ) + 4³  –  ( 16 : 2  – 1 ) · 5 – 150 : 5² . 

S o l u t i o n .  At first, powers must be calculated and changed by theirs values:

                                   ( 10 + 8 · 3 ) + 64 – ( 16 : 2 – 1 ) · 5 – 150 : 25 ;

                         after this, multiplication and division in the brackets and out of
                         them are executed:

                                             ( 10 + 24 ) + 64 – ( 8 – 1 ) · 5 – 6 ;

                         now, additions and subtractions in the brackets are executed:

                                                        34 + 64 – 7 · 5 – 6 ;

                         finally, after the rest of the multiplication 7 · 5 = 35 we receive:

                                                        34 + 64 – 35 – 6 = 57 .