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The given expression is:

\[
\sqrt[3]{(-3)^6 \cdot (-2)^3}
\]

After simplifying, the result is:

\[
18 \cdot (-1)^{\frac{1}{3}}
\]

This includes a cube root of \(-1\), which can be expressed in terms of complex numbers. However, if you're looking for a real number solution, the expression simplifies to 18 multiplied by a cube root of \(-1\), which is complex.

Would you like to explore the complex solution, or do you have any questions about this?

Here are 5 related questions:
1. What is the cube root of a negative number?
2. How does the cube root of a product simplify?
3. Why do powers of negative numbers often result in complex results?
4. How can we express cube roots of negative numbers in terms of real and imaginary parts?
5. What happens if the powers in the expression are different?

**Tip**: When working with cube roots of negative numbers, remember that they often involve complex numbers, since \((-1)^{1/3}\) doesn't yield a real number.

Simplify the expression: \(\sqrt[3]{(-3)^6 \cdot (-2)^3}\).

Explore how to simplify the expression \(\sqrt[3]{(-3)^6 \cdot (-2)^3}\). This problem covers concepts like exponents, cube roots, and introduces complex numbers. Ideal for high school students (Grades 9-12).

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