Solve [(5²-√16-72)²+√81]÷2: Complete Order of Operations Challenge

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 start by simplifying the expressions inside of the parentheses. Note that in the expression there are parentheses with division operations. Furthermore within these parentheses there is another set of inner parentheses with exponents. Hence we'll begin by simplifying the expression inside the inner parentheses according to the aforementioned order of operations,

First, we'll calculate the numerical value of the terms with exponents. Remember that according to the definition of a root as an exponent, the root is effectively an exponent. We'll perform the multiplication in the inner parentheses whilst continuing with the subtraction operations within these parentheses:

$\big((5^2-\sqrt{16}-7\cdot2)^2+\sqrt{81}\big):2= \\ \big((25-4-14)^2+\sqrt{81}\big):2= \\ \big(7^2+\sqrt{81}\big):2= \\$Continue to simplify the remaining parentheses (which were infact the outer ones), remembering that exponents precede addition and subtraction. Hence we will first calculate the numerical value of the terms with exponents in the parentheses and then proceed to perform the addition operation within the parentheses:

$\big(7^2+\sqrt{81}\big):2= \\ \big(49+9\big):2=\\ 58:2=\\ 29$ In the final stage, we performed the division operation,

Let's summarize the various steps of our solution , as shown below:

$\big((5^2-\sqrt{16}-7\cdot2)^2+\sqrt{81}\big):2= \\ \big(7^2+\sqrt{81}\big):2= \\ 58:2=\\ 29$ Therefore, the correct answer is answer D.