Question

a) 2 + 9² ÷ 3·2 - 1

Explanation:

Step1: Calculate the exponentiation

First, we calculate \(9^2\). According to the definition of exponentiation, \(9^2 = 9\times9 = 81\).

Step2: Perform the division

Next, we do the division operation \(81\div3\). \(81\div3 = 27\).

Step3: Perform the multiplication

Then, we multiply the result of the division by 2, that is \(27\times2 = 54\).

Step4: Perform the addition and subtraction

Finally, we do the addition and subtraction from left to right. First, \(2 + 54 = 56\), then \(56 - 1 = 55\). Wait, there may be a misinterpretation of the original expression. Let's re - examine the original expression: "2 + 9²÷3·2 - 1".

Step1: Calculate the exponent

Calculate \(9^2\), \(9^2=9\times9 = 81\).

Step2: Perform the division

Do the division \(81\div3 = 27\).

Step3: Perform the multiplication

Do the multiplication \(27\times2 = 54\).

Step4: Perform the addition and subtraction

First, \(2+54 = 56\), then \(56 - 1=55\).

Answer:

\(55\)