To find the cube root of \( -27x^9y^5 \), we take the cube root of each factor separately:

1. **Cube root of the constant term**:
   \[
   \sqrt[3]{-27} = -3
   \]

2. **Cube root of the \( x \) term**:
   \[
   \sqrt[3]{x^9} = x^{9/3} = x^3
   \]

3. **Cube root of the \( y \) term**:
   \[
   \sqrt[3]{y^5} = y^{5/3}
   \]

Combining these, the cube root of \( -27x^9y^5 \) is:
\[
-3x^3y^{5/3}
\]

### Final Answer:
\[
\sqrt[3]{-27x^9y^5} = -3x^3y^{5/3}
\]

Would you like further details on any part? 

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Here are some related questions to deepen understanding:

1. What is the cube root of a negative variable expression, such as \( -64a^{12}b^6 \)?
2. How does taking an even root (e.g., square root) differ when dealing with negative numbers compared to odd roots?
3. What would be the cube root of \( 27x^{12}y^9 \)?
4. How would the cube root of a fraction, like \( \frac{-27x^9}{y^6} \), be calculated?
5. How does exponent notation change when roots are applied to variables?

**Tip:** For roots of variable expressions, remember to apply the root to each term individually for clarity and accuracy.

Learn how to find the cube root of -27x^9y^5 with a clear, step-by-step breakdown. This problem covers essential algebraic concepts, including roots of constants and variables, exponent rules, and handling negative constants. Suitable for high school students in Grades 10-12.

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