infix to postfix doubt

Question

A * B ^ C + D becomes A B C ^ * D +

Here both the exponentiation and the multiplication must be done before the addition.

	current symbol	operator stack	postfix string
1	A		A
2	*	*	A
3	B	*	A B
4	^	* ^	A B
5	C	* ^	A B C
6	+	+	A B C ^ *
7	D	+	A B C ^ * D
8			A B C ^ * D +

in 4 line here precedence of     *   greater than  ^    therefore  *  should be popped out   , i checked precedence table too ,  someone explain this thanks 

Comments

Please check it again ! Precedence of Exponentiation operator is always greater than multiplication .

For example evaluate this expression 3*2^2?

---

bitwise xor sign is also  ^ and it has less precedence than * according to precedence table ?

Answer 1

Maybe you interpred wrongly please check precedence order again! ^ has always greater precedence than * ! and still you have doubt then associativity rule might be considered here.

Answer 2

1.Precedence of Exponentiation operator is always greater than multiplication.

2.Exponentiation  is right associative

3.Multiplication is left associative

apply

this rules and finds an answer.