What is the value of $3\cdot 3 + 3(3 + 3) - 3^3$?
To solve this problem, I need to apply the order of operations: parentheses, exponents, multiplication and division, and addition and subtraction. I start by simplifying what's inside the parentheses: $3(3 + 3) = 3(6) = 18$. Now I have $3\cdot 3 + 18 - 3^3$. Next, I apply the exponent: $3^3 = 3\cdot 3\cdot 3 = 27$. Now I have $3\cdot 3 + 18 - 27$. Then, I do the multiplication: $3\cdot 3 = 9$. Now I have $9 + 18 - 27$. Finally, I do the addition and subtraction: $9 + 18 - 27 = 27 - 27 = 0$. 