Let me analyze the image and solve the given problem.

The expression is:
$(-1)^4 \cdot (-3)^{-3} \cdot 9^2$

Step-by-step Calculation:

1. Simplify $(-1)^4$: Since $(-1)^4 = 1$, any negative number raised to an even power becomes positive.

   $(-1)^4 = 1$

2. Simplify $(-3)^{-3}$: A negative exponent means we take the reciprocal: $(-3)^{-3} = \frac{1}{(-3)^3}$ Calculate $(-3)^3$: $(-3)^3 = -27$ So: $(-3)^{-3} = \frac{1}{-27} = -\frac{1}{27}$

3. Simplify $9^2$: $9^2 = 81$

4. Combine the terms: Substitute the simplified values: $1 \cdot \left(-\frac{1}{27}\right) \cdot 81$ Simplify: $1 \cdot -\frac{1}{27} \cdot 81 = -\frac{81}{27}$

5. Simplify the fraction: $-\frac{81}{27} = -3$

Final Answer:

$\boxed{-3}$

Would you like a detailed explanation for any step?

Here are 5 questions you can explore next:

1. What happens if a negative number is raised to an odd power?
2. How do negative exponents work mathematically?
3. Can fractional exponents (like $x^{1/2}$) be calculated similarly?
4. How can you simplify expressions with multiple exponents and bases?
5. What are the properties of zero as an exponent?

Tip: Always simplify expressions with exponents step by step to avoid errors.