8. \( 15-7 \times 2+2^{3} \) 10. \( 6+3(13-2)-5^{2} \) 12. \( \frac{8+6^{2}}{11}+7 \times 2 \)

Did you know that the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), was first formalized in the 19th century? This system helps us avoid confusion and ensures everyone interprets mathematical expressions consistently—essential for things like engineering, computing, and beyond! When tackling calculations like these, it’s a common mistake to perform operations from left to right without recognizing when to prioritize! Always remember to resolve exponents first, followed by multiplication and division, and then finish with addition and subtraction. This approach will save you from any mathematical mishaps and keep your problem-solving sharp!