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.