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Let's break down the given expression step by step using the order of operations, also known as **PEMDAS** (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)):

### The given expression:
\[
2^2 - (6 + 4) + 1
\]

1. **Parentheses**: 
   First, evaluate the expression inside the parentheses:
   \[
   6 + 4 = 10
   \]
   So the expression becomes:
   \[
   2^2 - 10 + 1
   \]

2. **Exponents**: 
   Now, evaluate the exponent:
   \[
   2^2 = 4
   \]
   This gives:
   \[
   4 - 10 + 1
   \]

3. **Addition and Subtraction**: 
   Perform subtraction and addition from left to right:
   \[
   4 - 10 = -6
   \]
   Then:
   \[
   -6 + 1 = -5
   \]

Thus, the value of the expression is \(-5\).

---

Would you like more details on any specific step?

Here are 5 related questions to deepen your understanding:

1. What is the significance of using parentheses in an expression?
2. How would the result change if the exponent was different, for example, \(3^2\) instead of \(2^2\)?
3. Can you apply the order of operations to an expression with division, such as \(6 \div (2 + 1)\)?
4. Why is it important to follow the order of operations strictly?
5. How does subtraction behave differently when done before addition?

### Tip:
Always solve parentheses first in an expression to simplify calculations and avoid mistakes.

Evaluate the expression 2^2 - (6 + 4) + 1 using order of operations.

Learn how to evaluate the expression 2^2 - (6 + 4) + 1 step by step using the order of operations, which includes parentheses, exponents, addition, and subtraction. This solution is suitable for students in Grades 5-7.

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