To solve the expression \(-3^2 - 5(3) + 6\), follow the order of operations, commonly known as **PEMDAS** (Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right)):

### Step 1: Handle the exponentiation
\[
-3^2 = -(3^2) = -9
\]
Notice that the negative sign is not part of the exponent, so we first square \(3\) to get \(9\), then apply the negative sign.

Now the expression becomes:
\[
-9 - 5(3) + 6
\]

### Step 2: Handle the multiplication
\[
5(3) = 15
\]
So the expression becomes:
\[
-9 - 15 + 6
\]

### Step 3: Perform addition and subtraction from left to right
\[
-9 - 15 = -24
\]
\[
-24 + 6 = -18
\]

### Final answer:
\[
-3^2 - 5(3) + 6 = -18
\]

Would you like further details or clarifications?

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Here are 5 related questions to expand your understanding:
1. How does the order of operations (PEMDAS) affect solving this type of expression?
2. What happens if we change the negative sign in front of the exponent to inside the parentheses?
3. How do we handle expressions with more than one exponent?
4. What if the problem included division instead of multiplication—how would that change the steps?
5. How can we solve expressions with variables in addition to numbers?

**Tip:** Always remember that the negative sign outside an exponent only applies after performing the exponentiation.

Learn how to solve the expression -3² - 5(3) + 6 step-by-step using the order of operations (PEMDAS). This problem demonstrates handling exponents, multiplication, and subtraction with negative numbers. Suitable for students in Grades 6-8.

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