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When simplifying numerical expressions, calculating powers is often the first step. Powers are a way to express repeated multiplication. For example, when you see something like \(3^2\), it means \(3\) is being multiplied by itself two times, giving you \(3 \times 3 = 9\). Similarly, \(2^4\) means \(2\) is multiplied by itself four times: \(2 \times 2 \times 2 \times 2 = 16\). These calculations are crucial because they simplify parts of the expression, making it easier to tackle the next steps. Calculating powers first helps avoid mistakes that could arise from incorrect calculations with other operations. Always remember to complete calculations of powers before moving on to other operations in your expression.
It's like breaking down a complicated task into smaller, manageable parts.

After calculating powers, the next step is often to perform addition or subtraction. In our example, we have the expression \(9 - 16\). In subtraction, the order of numbers matters; you subtract the second number from the first. Here, 16 is subtracted from 9. Subtraction can sometimes lead to negative numbers, as is the case in this example, where the result is \(-7\).
Understanding that numbers can be negative, and learning how to handle them, is an important skill in mathematics. Additionally, it’s helpful to keep an eye out for negative signs and ensure they are handled correctly.

• Always line up numbers carefully when subtracting.
• Check your answer for negative results; if the smaller number is subtracted from a larger one, expect a negative result.

Subtraction can tie together separate powers calculations, making it an integral part of simplifying expressions.

Order of operations is a fundamental concept in algebra and arithmetic, ensuring that everyone performs calculations the same way. Commonly remembered by the acronym PEMDAS- Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right) - it guides us on the correct sequence to solve a mathematical expression.
In our exercise, we start with the exponent calculation, following the priority from PEMDAS, resulting in \(3^2\) and \(2^4\), before moving to subtraction. By adhering to the order of operations, you avoid errors and ensure that the expression is simplified as intended.

• Always handle operations inside parentheses first, though in our case, none were present.
• Calculate exponents next, as shown in our example.
• Proceed with multiplication or division, and then addition or subtraction as encountered in order from left to right.

Understanding and applying the order of operations ensures clarity and correctness in mathematical problem-solving.