https://file.aiquickdraw.com/mathbot/file/17259999534390kjkxbb1.jpg

give an answer and tell the rules you used 

The expression given in the image is:

\[
-7^2 - (-2)^3
\]

### Step-by-Step Solution:

1. **Evaluate the exponentiation:**

   - \(7^2 = 7 \times 7 = 49\)
   - \((-2)^3 = (-2) \times (-2) \times (-2) = -8\)

2. **Apply the signs:**

   - The first term is \(-7^2\), which is \(-49\) (because the negative sign in front is not affected by the exponent).
   - The second term is \(-(-2)^3\), which is \(-(-8) = 8\).

3. **Combine the results:**

   \[
   -49 + 8 = -41
   \]

### Final Answer:
\[
-41
\]

### Rules Used:

1. **Order of Operations (PEMDAS/BODMAS):** Exponentiation is performed before multiplication, division, addition, and subtraction.
2. **Handling Negative Signs:** The negative sign in front of a number is applied after the exponentiation. For example, \(-7^2\) means you square 7 first (getting 49), then apply the negative sign to get \(-49\).

Would you like more details on any step or have any questions?

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### Related Questions:
1. What is the result of \(-5^2 - 3^3\)?
2. How does the order of operations affect expressions with multiple exponents?
3. What is the value of \((-4)^2 - (-3)^3\)?
4. How would the result differ if the expression was \((-7)^2 - (-2)^3\)?
5. Can you solve \(-6^2 + 2^4\) and explain the steps?

### Tip:
Always apply exponents before applying the negative sign if the negative sign is outside the parentheses.

Learn how to solve the expression -7^2 - (-2)^3 by applying exponentiation and handling negative signs. A step-by-step guide suitable for Grades 6-8, covering key concepts such as exponentiation and the order of operations.

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