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The problem asks you to evaluate the exponential expression:

\[
6 \cdot (4 + 2)^2 - 3^2
\]

Let's solve this step by step:

### Step 1: Simplify the parentheses
\[
4 + 2 = 6
\]

So the expression becomes:
\[
6 \cdot 6^2 - 3^2
\]

### Step 2: Calculate the exponents
\[
6^2 = 36 \quad \text{and} \quad 3^2 = 9
\]

Substitute these values into the expression:
\[
6 \cdot 36 - 9
\]

### Step 3: Perform multiplication
\[
6 \cdot 36 = 216
\]

Now the expression is:
\[
216 - 9
\]

### Step 4: Perform subtraction
\[
216 - 9 = 207
\]

### Final Answer:
The value of the expression is:
\[
\boxed{207}
\]

Would you like more details on any part of the solution?

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### Related Questions:
1. What is the importance of the order of operations in evaluating expressions?
2. How does squaring a number affect its magnitude compared to the base?
3. Can this problem be solved using different grouping methods? Why or why not?
4. What happens if parentheses are missing in similar expressions?
5. How can we double-check solutions to similar mathematical expressions?

### Tip:
Always handle exponents before multiplication and subtraction when solving such problems to avoid errors.

Evaluate the exponential expression: 6 * (4 + 2)^2 - 3^2.

Learn how to solve the exponential expression 6 * (4 + 2)^2 - 3^2 with a detailed breakdown of each step. Perfect for students in Grades 6-8, this example covers order of operations and exponentiation.

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