The expression to simplify is:

$\left( \frac{x^3 y^{-3}}{x^2 y} \right)^{-3}$

Let's break down the simplification step by step:

Step 1: Simplify the expression inside the parentheses

We can simplify the fraction inside the parentheses by applying the laws of exponents:

$\frac{x^3 y^{-3}}{x^2 y} = x^{3-2} y^{-3-1} = x^1 y^{-4}$

This simplifies to:

$x y^{-4}$

Step 2: Apply the exponent of $-3$

Now, apply the exponent $-3$ to the simplified expression $x y^{-4}$:

$(x y^{-4})^{-3} = x^{-3} y^{12}$

Final Simplified Expression:

$x^{-3} y^{12}$

Would you like more details on any of the steps or have any further questions?

Here are five related questions for practice:

1. How do you simplify expressions with negative exponents?
2. What happens when you raise a product of terms to a power?
3. Can you simplify $\left( \frac{x^2}{y^{-1}} \right)^{-2}$?
4. How do you divide powers of the same base with different exponents?
5. What is the difference between applying exponents to a single term versus multiple terms?

Tip: When simplifying expressions, always handle negative exponents carefully by converting them into positive exponents whenever possible!