https://file.aiquickdraw.com/mathbot/file/1730074568956opltnlk9.jpg

To solve the expression

\[
(-1)^4 \cdot (-3)^{-3} \cdot 9^2
\]

we will evaluate each term separately and then multiply the results.

1. **Calculate \( (-1)^4 \):**
   \[
   (-1)^4 = 1
   \]
   since raising \(-1\) to an even power results in \(1\).

2. **Calculate \( (-3)^{-3} \):**
   \[
   (-3)^{-3} = \frac{1}{(-3)^3} = \frac{1}{-27} = -\frac{1}{27}
   \]

3. **Calculate \( 9^2 \):**
   \[
   9^2 = 81
   \]

Now, we combine the results:
\[
1 \cdot \left(-\frac{1}{27}\right) \cdot 81 = -\frac{81}{27} = -3
\]

### Final Answer:
\[
-3
\]

Would you like further details or have any questions?

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Here are 5 related questions to practice:

1. What is \( (-1)^5 \cdot (-3)^{-2} \cdot 9^3 \)?
2. How would the result change if the exponent on \((-3)\) were positive?
3. Evaluate \( (-2)^4 \cdot (-5)^{-2} \cdot 6^3 \).
4. Calculate \( (-1)^3 \cdot (-2)^{-4} \cdot 5^2 \).
5. What is \( (-4)^3 \cdot (-3)^{-1} \cdot 2^4 \)?

**Tip:** Remember that raising a negative number to an even power yields a positive result, while raising it to an odd power yields a negative result.

Solve the expression (-1)^4 · (-3)^-3 · 9^2 by evaluating each term: exponentiation of integers, handling negative exponents, and multiplying results. Suitable for students in Grades 8-10.

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