91Ó°ÊÓ

In prealgebra, one of the basic concepts is **variable substitution**. This involves replacing a variable with a given number.
For example, in the expression \(-n^2\) where \(n = -9\), we substitute the variable \(n\) with \(-9\). This gives us the new expression \(-(-9)^2\).

• Always ensure that you substitute the variable correctly.
• Keep the replacement number in parentheses, especially if it is negative, to avoid confusion.

This step is crucial because any mistake in substitution can alter the entire calculation. Remember, accuracy in substitution lays the foundation for the correct evaluation of the expression.

When working with expressions involving exponents, remember that squaring a negative number results in a positive number. This is because: \[ (-a)^2 = a \times a \].

In our example, we needed to evaluate \((-9)^2\). Since \(-9 \times -9 = 81\), the answer to \( (-9)^2 \) is \ 81\.

• Always enclose the negative number in parentheses.
• Understand that the square of any number, whether positive or negative, will always be positive.

For deeper understanding, try to square other negative numbers and observe the results. This practice solidifies the concept and ensures you won't make mistakes in more complex problems.

The **order of operations** is a fundamental principle in mathematics that dictates the sequence in which operations should be performed to correctly evaluate expressions.

The standard sequence is often summarized by the acronym PEMDAS:

• Parentheses
• Exponents (like square roots and squaring)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Applying this to our example, we first tackle the **parentheses** and the **exponentiation** within: \(-(-9)^2\).

Next, we move to exponents: calculating \ (-9)^2 \ converts to \ 81 \.

Finally, we apply the **multiplication** or **division** outside, leading us to apply the negative sign outside the squared result: \ -81 \. This organization prevents errors and ensures correct results each time.

Practice using the PEMDAS rule to solidify your understanding of the order of operations.