Solve: 3+[5·4-(9·1+3)]-8 Using Order of Operations

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of these,

Therefore, we'll start by simplifying the expressions in parentheses. In this problem, there are parentheses within parentheses, so we'll first deal with the inner parentheses, simplify the expression within them and continue similarly with the outer parentheses and simplify the expression within them. We'll do all of the above while maintaining the order of operations mentioned at the beginning of the solution:

$3+[5\cdot4-(9\cdot1+3)]-8= \\ 3+[5\cdot4-(9+3)]-8= \\ 3+[5\cdot4-12]-8= \\ 3+[20-12]-8= \\ 3+8-8= \\ 3$

Note that since multiplication and division come before addition and subtraction, in the first stage, we first performed the multiplication in the inner parentheses and then performed the addition, and continued similarly with the expression we got after opening these parentheses which was in the outer parentheses, first we performed the multiplication in the first term in the outer parentheses, and then the subtraction within them, finally, after opening the outer parentheses we performed the addition and subtraction operations,

Therefore we got that answer C is the correct answer.