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Understanding the order of operations is crucial when simplifying mathematical expressions. It determines the sequence in which operations should be performed to solve an expression correctly. The standard order, often remembered by the acronym PEMDAS, stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It's essential to follow this sequence to avoid errors in calculation.

To illustrate, let's take the given exercise: Simplifying the expression involves following these rules strictly. We first address any multiplications or divisions as they appear from left to right before moving to addition and subtraction. This sequential approach ensures that all parts of the expression are handled systematically, which is illustrated step by step in the provided solution.

Arithmetic operations form the foundation of most mathematical problems and include addition, subtraction, multiplication, and division. When performing these operations, it's vital to understand their respective properties, such as commutativity (order doesn't matter for addition and multiplication), associativity (grouping doesn't matter for addition and multiplication), and distributivity (how multiplication distributes over addition and subtraction).

In our exercise, each step demonstrates a single arithmetic operation executed in isolation. This approach helps grasp the immediate result of each operation. The step-by-step solution breaks down the often automatic process of simplification, reinforcing understanding of each arithmetic operation and its impact on the overall expression.

To solve algebraic expressions, one must apply the same principles of order of operations and arithmetic operations as with numerical expressions. An algebraic expression may include variables, and the goal is often to isolate these variables by performing operations on both sides of the equation. The key is to do so in a systematic and legal manner, respecting the mathematical laws. Simplifying expressions first makes it easier to isolate variables when you proceed to equations.

Although the given exercise doesn't have variables, the steps undertaken to simplify it are relevant for algebraic expressions. Each arithmetic action is akin to puzzle-solving, where the simplification process reveals the most straightforward form of the expression, akin to isolating a variable in algebraic expressions.