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

Proceed to simplify the given 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 begin by simplifying the expressions inside of the parentheses. This should be carried out according to the order of operations mentioned above. We'll calculate the numerical value of the term with the exponent, which is the divided term inside of the parentheses. Simultaneously we'll calculate the result of the multiplication inside of the parentheses. Then we'll proceed to calculate the addition operation:

$65-(4\cdot3+2^3:4)-4^3+5^2:5= \\ 65-(12+8:4)-4^3+5^2:5=\\ 65-(12+2)-4^3+5^2:5=\\ 65-14-4^3+5^2:5=\\$Simplify the resulting expression. Proceed to calculate the numerical value of the term with the exponent, which is the third term from the left. At the same time we will calculate the numerical value of the term with the exponent, which is divided by the fourth term from the left. We'll then continue to perform the division operation on this term. This is due to the fact that multiplication and division precede 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 as shown below:

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