The expression in the image is:

$\left( \frac{2a^{-2}}{b^{-3}} \right)^{-3}$

To simplify, let's break it down step by step:

1. Apply the exponent to the fraction and each term inside: $\left( \frac{2a^{-2}}{b^{-3}} \right)^{-3} = \frac{(2a^{-2})^{-3}}{(b^{-3})^{-3}}$

2. Simplify each part:

   • $(2a^{-2})^{-3} = 2^{-3} \cdot a^{6} = \frac{1}{8} \cdot a^6 = \frac{a^6}{8}$
   • $(b^{-3})^{-3} = b^{9}$

3. Substitute back into the fraction: $\frac{a^6}{8} \cdot \frac{1}{b^9} = \frac{a^6}{8b^9}$

Thus, the simplified expression is:

$\frac{a^6}{8b^9}$

Would you like more clarification or have additional questions?

Here are some related questions to explore further:

1. How do negative exponents affect the simplification process?
2. What is the significance of a negative exponent in a fraction?
3. How do we handle exponents when simplifying fractions in algebra?
4. Can we apply similar steps to simplify expressions with more complex powers or variables?
5. What role does the distributive property play when dealing with exponents?

Tip: Remember that when raising a fraction to a power, you apply the exponent to both the numerator and denominator individually!