Infix vs postfix vs prefix - which has the smallest processing time
You can express the same in prefix and postfix without brackets. 

For example, a + b * c can be ambiguous so it can give 2 different results so you need some precedence to solve the expression(as you have mentioned BODMAS) but both the trees if traveled in prefix or postfix leads to a unique results like (a + b) * c will have postfix ab+c* and a + (b * c) will have abc*+.