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The given expression is:

\[
(a - b)^3 \cdot \left( \frac{a + b}{b - a} \right)^{-2}
\]

### Step 1: Simplify the second part
The expression \(\frac{a + b}{b - a}\) can be rewritten as:

\[
\frac{a + b}{b - a} = - \frac{a + b}{a - b}
\]

Thus, the second part becomes:

\[
\left( \frac{a + b}{b - a} \right)^{-2} = \left( - \frac{a + b}{a - b} \right)^{-2} = \frac{(a - b)^2}{(a + b)^2}
\]

### Step 2: Multiply the two terms
Now, the entire expression becomes:

\[
(a - b)^3 \cdot \frac{(a - b)^2}{(a + b)^2}
\]

### Step 3: Combine powers of \((a - b)\)
Using the property of exponents, \((a - b)^3 \cdot (a - b)^2 = (a - b)^5\), the expression simplifies to:

\[
\frac{(a - b)^5}{(a + b)^2}
\]

Thus, the simplified expression is:

\[
\boxed{\frac{(a - b)^5}{(a + b)^2}}
\]

Would you like any further details or have any questions about the steps? 

Here are some related questions to practice:

1. How do you simplify powers when multiplying terms with the same base?
2. What is the general rule for negative exponents?
3. How do you handle a fraction raised to a negative power?
4. Can you provide another example of combining powers with the same base?
5. What happens when simplifying expressions involving both powers and negative signs?

**Tip**: Always pay attention to signs when working with expressions like \((a - b)\) and \((b - a)\) since they are negatives of each other!

Learn how to simplify algebraic expressions like (a - b)^3 * ((a + b) / (b - a))^(-2) with step-by-step guidance. This problem covers key algebraic concepts, including exponent rules and handling negative powers. Suitable for students in Grades 9-12.

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