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The order of operations is a set of rules guiding us on which calculations to perform first in a mathematical expression. One popular acronym for this set of rules is PEMDAS. Memorizing PEMDAS can be a powerful tool to solve expressions correctly every time. PEMDAS stands for:

• Parentheses
• Exponents (powers and roots, etc.)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

When you are simplifying expressions, always look for these operations in the PEMDAS order, starting from the top of the list and working your way to the bottom. This method ensures that you do not make mistakes by performing calculations out of order, which could lead to wrong answers.

Multiplication and addition are two of the core operations in arithmetic. When simplifying expressions that involve both operations, like our example expression: \[5 \cdot 2 + 9 \cdot 8\]it's important to follow the PEMDAS rule so that you apply multiplication before addition.**Understanding the Operations:**- **Multiplication:** This operation can be thought of as repeated addition. For instance, multiplying 5 by 2 (written as \(5 \cdot 2\)) means adding 5 to itself 2 times, resulting in 10.- **Addition:** This operation combines numbers to form a sum. In our case, adding 10 and 72 gives a sum of 82.Remember, always complete all multiplication operations in an expression before moving on to any addition operations. This makes simplifying more effective and error-free.

Simplifying expressions involves following certain rules to shorten or condense the expression to its simplest form. Let's go through the simplification process step by step using the expression:\[5 \cdot 2 + 9 \cdot 8\]**Step-by-Step Simplification:**1. **Identify Operations:** Look at the expression you have. What operations are present? Here, we see multiplication and addition.2. **Apply PEMDAS:** Following the order of operations, we first solve: - Multiplication: \(5 \cdot 2 = 10\) and \(9 \cdot 8 = 72\) 3. **Substitute and Simplify:** Replace the multiplications in the expression with their results: \(10 + 72\)4. **Perform the Addition:** Finally, add them together to get \(82\)By breaking it down into smaller steps and using the order of operations, the simplification process becomes much easier and less daunting.