Solve Complex Expression: 96-64÷((5+13)÷9×4)+48 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 them,

Therefore, we'll start by simplifying the expressions in parentheses, noting that in this expression there are parentheses within parentheses, so we'll begin by simplifying the expression in the innermost parentheses and perform the addition operation within them:

$96-64:\big((5+13):9\cdot4\big)+48= \\ 96-64:\big(18:9\cdot4\big)+48$

Next, we'll perform the division and multiplication operations that remain in the parentheses, we'll do this according to the natural order of operations from left to right, since there are no additional parentheses in this expression (within the parentheses) dictating a different order of operations, and between these two operations there is no defined order as mentioned above, therefore we'll first perform the division operation and then the multiplication operation:

$96-64:\big(18:9\cdot4\big)+48=\\ 96-64:\big(2\cdot4\big)+48=\\ 96-64:8+48$

We'll continue and remember that multiplication and division come before addition and subtraction, therefore we'll first perform the division operation and only in the next step the subtraction and addition operations:

$96-64:8+48 =\\ 96-8+48 =\\ 136$

Let's summarize the steps of simplifying the expression:

$96-64:\big((5+13):9\cdot4\big)+48= \\ 96-64:\big(18:9\cdot4\big)+48=\\ 96-64:8+48 = \\ 136$

Therefore, the correct answer is answer B.