The simplified form of the expression $(3i)^3 \times (-2i)^2$ is $108i$.

Would you like a detailed explanation, or do you have any further questions?

Here are some related questions to deepen understanding:

1. How do you calculate powers of complex numbers like $i^3$ or $i^2$?
2. What is the general rule for simplifying powers of imaginary numbers?
3. Can you break down each step in simplifying $(3i)^3$?
4. How do you apply the distributive property when multiplying complex numbers?
5. What happens if we multiply two complex numbers with both real and imaginary parts?

Tip: Remember that $i^2 = -1$, which is key when working with powers of imaginary numbers.