# 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 executed
*
according 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 + 2
^{
3
}
·
3 ) + 4
^{
3
}
– ( 16 : 2 – 1 )
·
5 – 150 : 5
^{
2
}
.

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 .