>>106029566>except for this one thing???
Allow me to rephrase.
You start with P, left-to-right. You then do E, left-to-right. You then do M/D, left-to right. You then do A/S, left-to right.
The longer version is that you begin by reading left-to-right looking for P(arentheses), and solve whatever is in the parentheses, from left-to-right, beginning with whatever P(arentheses) may be within, and whatever other P(arentheses may be within those parentheses, etc - once you have isolated sub-expressions completely unmolested by parentheses, you then apply exponents, reading left-to right. You then apply multiplication and division, reading left-to right. You then apply addition and subtraction, reading left to right. Once everything within the parentheses has been solved, you may solve the overall problem, starting with exponents (read from left-to-right), then multiplication and division (read from left-to-right), then finally addition and subtraction (read from left-to-right). It is a consistent and logical system that does not break its own rules at any point.