Solve: 65-(4×3+2³÷4)-4³+5²÷5 Order of Operations Challenge

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, we'll do this according to the order of operations mentioned above, first we'll calculate the numerical value of the term with the exponent, which is the divided term in parentheses, and simultaneously we'll calculate the result of the multiplication in parentheses, then we'll calculate the addition in them:

$65-(4\cdot3+2^3:4)-4^3+5^2:5= \\ 65-(12+8:4)-4^3+5^2:5=\\ 65-(12+2)-4^3+5^2:5=\\ 65-14-4^3+5^2:5=\\$We'll continue and simplify the resulting expression, first we'll calculate the numerical value of the term with the exponent, which is the third term from the left, simultaneously we'll calculate the numerical value of the term with the exponent which is divided by the fourth term from the left and we'll continue to perform the division operation on this term, this is because multiplication and division come before addition and subtraction:

$65-14-4^3+5^2:5=\\ 65-14-64+25:5=\\ 65-14-64+5$$$We'll finish simplifying the given expression and perform the addition and subtraction operations:

$65-14-64+5 =\\ -8$Let's summarize the steps of simplifying the given expression, we got that:

$65-(4\cdot3+2^3:4)-4^3+5^2:5= \\ 65-(12+8:4)-4^3+5^2:5=\\ 65-14-64+5 =\\ -8$Therefore, the correct answer is answer C.