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When dealing with mathematical expressions, the order in which you perform operations is critical. This is famously remembered by the acronym "PEMDAS," which stands for:

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

It is important to perform operations within parentheses first, followed by exponents, then perform all multiplication and division from left to right, and finally handle addition and subtraction from left to right. This way ensures that everyone arrives at the same result for a given expression.

In the given problem \(-9+[-6+(-4)]\), the presence of parentheses indicates that the operations inside should be executed first. Using the proper order prevents miscalculations and errors, ensuring accurate results every time.

Evaluating expressions involves breaking down a complex mathematical problem into simpler parts using the rules and operations necessary to reach a result. It's like simplifying your problem one step at a time.

Consider the expression: \(-9+[-6+(-4)]\). To evaluate it effectively:

• Start by resolving any mathematical operations within the innermost parentheses.
• In this example, \(-6 + (-4)\) is inside the first parentheses. Solve it first to get \(-10\).
• Replace the original expression with the result of this calculation, resulting in a simpler \(-9 + (-10)\).
• Then, perform the remaining operations step by step following the order of operations.

This systematic approach simplifies expressions to make them more manageable and easier to solve.

Parentheses are crucial tools in mathematics that dictate the sequence of operations in an expression. They help to organize calculations and clarify which operations take precedence. Without them, performing calculations accurately would be near impossible.

In the expression provided, \(-9+[-6+(-4)]\), parentheses were used twice, creating a nested format. The inner parentheses prioritize the calculation of \(-6+(-4)\), which is solved first because of its arrangement. By calculating the sum within, we simplify part of the problem right away.

Subsequently, the square brackets, which also function as parentheses, contain the result of the previous computation, allowing you to handle the next operation systematically. Therefore, -9 + (-10) is a short and direct calculation. This usage of parentheses ensures that every mathematical expression is evaluated accurately and consistently.