Evaluate [(3^4-8+5):(6^2+√9)]-[√64-4^2]: Complete Expression Solution

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 two pairs of parentheses with subtraction between them, and also that within the left parentheses there are two more pairs of inner parentheses with division between them, so we'll start by simplifying the expressions within the parentheses, both the expression in the inner parentheses with division between them that are inside the outer left parentheses, and the expression in the right parentheses, this is done according to the order of operations mentioned above:

$\big((3^4-8+5):(6^2+\sqrt{9})\big)-(\sqrt{64}-4^2)= \\ \big((81-8+5):(36+3)\big)-(8-16)= \\ 78:39-(-8)\\$We simplified the above expressions (those within the parentheses) while remembering that exponents come before addition and subtraction, so first we calculated the numerical values of the terms with exponents (while remembering that according to the definition of root as an exponent, the root is an exponent for all purposes) and then we performed the addition and subtraction operations within the parentheses,

In the final stage, since the result of the subtraction operation in the right parentheses yielded a negative result, we kept this result in parentheses, which we will open in the next stage, while remembering that according to the multiplication law, multiplying a negative number by a negative number gives a positive result,

Let's continue then and simplify the expression we got in the last stage:

$78:39-(-8)=\\ 2+8=\\ 10$We simplified the expression where in the first stage we performed the division operation in the first term from the left and simultaneously opened the parentheses on the right (this is according to the multiplication law as mentioned before) and this is because multiplication and division come before addition and subtraction, then we performed the addition operation,

Therefore the correct answer is answer A.