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The given expression is \(-x^2\) with \(x = -9\). Let's evaluate the expression step by step:

1. First, substitute \(x = -9\) into the expression \(-x^2\):
   \[
   -( (-9)^2 )
   \]

2. Next, calculate \((-9)^2\):
   \[
   (-9) \times (-9) = 81
   \]

3. Now, apply the negative sign:
   \[
   -(81) = -81
   \]

Thus, the expression evaluates to \(-81\).

Would you like further details or have any questions? Here are five related questions:

1. What happens if \(x = 9\) instead of \(-9\) in the same expression?
2. How would the result change if the negative sign were inside the square, i.e., \((-x)^2\)?
3. Can you explain the difference between squaring a positive number versus squaring a negative number?
4. How would the result differ for other values of \(x\) such as \(x = 0\)?
5. How does the negative sign outside the square affect the result?

**Tip**: Always apply the exponent before applying any other operations like multiplication or addition when working with algebraic expressions.

Learn how to evaluate the expression -x^2 when x = -9. This problem involves applying exponentiation and dealing with negative numbers. The solution uses fundamental algebraic concepts like exponents and the order of operations. Ideal for students in Grades 6-8.

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