\( 1.1 .22 ( 4 \div 0.2 ) ^ { 3 } - 108 \)

Let's break it down step by step! First, calculate the expression inside the parentheses: \(4 \div 0.2\) which equals \(20\). Then, raise \(20\) to the power of \(3\), giving us \(8000\). Now, multiply \(1.1\) by \(0.22\), which equals \(0.242\), and then multiply that by \(8000\) to get \(1936\). Lastly, subtract \(108\) to arrive at \(1828\). So the final answer is \(1828\)! This problem showcases the importance of mastering the order of operations, also known as PEMDAS/BODMAS! Understanding this rule can make complex calculations a breeze by providing a structured way to approach math problems. Whether you're juggling numbers in your head or on paper, remembering to process parentheses and exponents before moving to multiplication or subtraction can save you time and frustration.