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To solve the expression \( (3 + 7)^2 + 9 \), let's break it down step by step:

1. **First, evaluate inside the parentheses**:
   \[
   3 + 7 = 10
   \]

2. **Next, square the result**:
   \[
   10^2 = 100
   \]

3. **Finally, add 9 to the squared result**:
   \[
   100 + 9 = 109
   \]

Thus, the value of \( (3 + 7)^2 + 9 \) is **109**.

Would you like further clarification on any of these steps?

Here are some related questions you might find helpful:
1. What happens if you change the numbers in the parentheses?
2. How do you handle powers of negative numbers in similar problems?
3. How would the process change with a cube instead of a square?
4. What if you needed to subtract instead of add in the parentheses?
5. How can this expression be generalized for variables?

**Tip**: Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) when solving complex expressions.

Learn how to solve the arithmetic expression (3 + 7)^2 + 9 with step-by-step instructions. This problem covers key math concepts like addition, exponents, and the order of operations. Suitable for students in Grades 6-8.

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