https://file.aiquickdraw.com/mathbot/file/17299903390909oro4g9o.jpg

The expression provided in the image is:

\[
(-3)^4 + (-3)^6 \div (-3)^5 - (-3)^2
\]

### Step-by-Step Solution

1. **Evaluate each term separately:**
   - \((-3)^4\): Since \(4\) is an even power, \((-3)^4 = 81\).
   - \((-3)^6\): Since \(6\) is also an even power, \((-3)^6 = 729\).
   - \((-3)^5\): Since \(5\) is an odd power, \((-3)^5 = -243\).
   - \((-3)^2\): With an even power, \((-3)^2 = 9\).

2. **Perform the division:**
   - \(\frac{(-3)^6}{(-3)^5} = \frac{729}{-243} = -3\).

3. **Substitute values back into the expression:**

   \[
   81 + (-3) - 9
   \]

4. **Calculate the final result:**

   - \(81 - 3 = 78\)
   - \(78 - 9 = 69\)

### Final Answer
\[
69
\]

Would you like further details or have any questions?

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### Related Questions

1. How would the solution change if \((-3)\) were raised to an odd power in each term?
2. Can you explain why raising a negative number to an even power results in a positive value?
3. How does the order of operations affect expressions with powers and division?
4. What would the result be if all terms used positive 3 instead of \(-3\)?
5. How can exponents be simplified when using division in expressions?

### Tip
When dealing with powers of negative numbers, remember that an even exponent results in a positive outcome, while an odd exponent keeps the result negative.

Understand how to solve the expression (-3)^4 + (-3)^6 ÷ (-3)^5 - (-3)^2 with step-by-step calculations. This problem involves key mathematical concepts such as exponents, the division of exponents, and operations with negative bases, suitable for students in Grades 8-10.

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