Solve Complex Expression: 96-64÷((5+13)÷9×4)+48 Using Order of Operations

Simplify this expression whilst following the order of operations . The order of operations states that exponents precede multiplication and division, which in turn precede addition and subtraction, and that parentheses precede all of the above:

Therefore, we'll start by simplifying the expressions inside of the parentheses. Note that in this expression there are parentheses within parentheses. Begin by simplifying the expression in the innermost parentheses and perform the addition operation within them:

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

Proceed to the division and multiplication operations that remain inside of the parentheses.

Follow the natural order of operations from left to right, given that there are no additional parentheses in this expression (within the parentheses) as well as no defined order as mentioned above. Therefore we'll first perform the division operation and then the multiplication operation:

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

Remember that multiplication and division precede 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.