Solve ((5-4·3)²+8-3)÷2: Complete Order of Operations Practice

This expression is simplified while maintaining the order of operations which states that parentheses take come before exponents, and the exponents come before multiplication and division which come before addition and subtraction.

Therefore, we will start first by simplifying the expressions in the parentheses, in this case there are parentheses within parentheses, so we will first deal with the inner parentheses.

We will simplify the expression within the innermost parentheses and then we will perform the exponentiation on them, then we will deal similarly with the outer parentheses while maintaining the order of operations:

$\big((5-4\cdot3)^2+8-3\big):2= \\ \big((5-12)^2+8-3\big):2= \\ \big((-7)^2+8-3\big):2= \\ \big(49+8-3\big):2=\\$Note that since exponents come before multiplication and division we first performed the exponentiation in the outer parentheses and then the division operation, we continued and performed first the exponentiation of the expression results in the inner parentheses by squaring. (Remember that raising any number (positive or negative) to an even, positive power will always give a positive result).

We continue and finish dealing with the expression in the remaining parentheses, then we perform the division operation that applies to the parentheses:

$\big(49+8-3\big):2=\\ 54:2=\\ 27$In summary of the solution steps, we found that:

$\big((5-4\cdot3)^2+8-3\big):2= \\ \big((5-12)^2+8-3\big):2= \\ \big(49+8-3\big):2=\\ 27$Therefore, the correct answer is answer a.