b. 102 + 2 . 42 − (52+ 70 ) + (−1) + (−3)2=

Let's solve the expression step by step.

Given:
\[
102 + 2 \cdot 42 - \left(52 + 70\right) + (-1) + (-3)^2
\]

1. **Handle the operations inside the parentheses:**
   - \( 52 + 70 = 122 \)

   The expression now becomes:
   \[
   102 + 2 \cdot 42 - 122 + (-1) + (-3)^2
   \]

2. **Calculate the powers and multiplication:**
   - \( (-3)^2 = 9 \)
   - \( 2 \cdot 42 = 84 \)

   The expression now becomes:
   \[
   102 + 84 - 122 + (-1) + 9
   \]

3. **Perform the addition and subtraction from left to right:**
   - \( 102 + 84 = 186 \)
   - \( 186 - 122 = 64 \)
   - \( 64 + (-1) = 63 \)
   - \( 63 + 9 = 72 \)

The final answer is:
\[
\boxed{72}
\]

Would you like further details on any part of this solution?

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Here are 5 related questions to expand your understanding:

1. How would the result change if the power of \(-3\) was odd instead of even?
2. What if the subtraction sign in front of \(122\) was a different operation?
3. How do different orders of operations affect the final result?
4. Can you rewrite the expression to change the order in which operations are performed?
5. How does changing a single number affect the overall calculation?

**Tip:** Always be cautious with negative signs and exponents—they can significantly alter your results!

Learn how to solve the arithmetic expression 102 + 2 * 42 - (52 + 70) + (-1) + (-3)^2 step-by-step. This problem covers arithmetic operations including addition, multiplication, parentheses handling, and exponentiation. Suitable for students in Grades 7-9.

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