Use the order of operations to simplify the given expression. \[ (4+5)^{2} \div 3 \]

First, let's simplify the expression inside the parentheses. So, \(4 + 5\) equals \(9\). Now we have \(9^2 \div 3\). Next, we calculate \(9^2\), which gives us \(81\). Finally, we take \(81 \div 3\) which equals \(27\). Thus, the simplified expression is \(27\). Did you know that the order of operations can be remembered by the acronym PEMDAS? It stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right) - making it a handy tool for math lovers! If you're ever feeling stuck with order of operations, a tip is to write down each step as you go, which helps you keep track of what you’ve done and what you need to do next. A common mistake is rushing through the steps, especially with exponents and ignoring the division that follows. Slow and steady wins the math race!