Solve [(5²-√16-72)²+√81]÷2: Complete 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 these,

Therefore, we'll start by simplifying the expressions in parentheses, noting that in the expression there are parentheses with division operations, and also note that within these parentheses there is another set of inner parentheses with exponents, so we'll start 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, while remembering that according to the definition of a root as an exponent, the root is an exponent for all purposes, simultaneously we'll perform the multiplication in the inner parentheses and continue with the subtraction operations within these parentheses:

$\big((5^2-\sqrt{16}-7\cdot2)^2+\sqrt{81}\big):2= \\ \big((25-4-14)^2+\sqrt{81}\big):2= \\ \big(7^2+\sqrt{81}\big):2= \\$We'll continue and simplify the remaining parentheses (which were actually the outer ones), remembering that exponents come before addition and subtraction, so first we'll calculate the numerical value of the terms with exponents in the parentheses and then 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 steps of simplifying the given expression, we got that:

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