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.