According to operator rules, what is the calculation priority for expressions within parentheses?

Expressions within parentheses have the highest priority in calculations, meaning they are always calculated first. This is a fundamental rule in operator precedence that ensures clarity and accuracy in mathematical and programming expressions. By prioritizing calculations within parentheses, you can dictate the order in which operations are performed, which can significantly affect the outcome. For instance, in the expression (3 + 2 \times (5 - 1)), evaluating the parentheses first gives (5 - 1) which equals 4, leading to (3 + 2 \times 4) and then correctly applying multiplication before addition based on the rules of precedence.

Using parentheses allows for complex expressions to be broken down into simpler parts, ensuring the intended operations are performed in the correct order. This principle is integral to both mathematics and programming languages, helping to avoid ambiguity in operations.