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The expression given is:

\[
\left(-4v^2 u^3\right)^3
\]

To simplify this expression, we apply the exponent to each term inside the parentheses:

1. **Apply the exponent to the constant term:**  
   \((-4)^3 = -64\)  
   
2. **Apply the exponent to the variable \(v^2\):**  
   \((v^2)^3 = v^{2 \times 3} = v^6\)  
   
3. **Apply the exponent to the variable \(u^3\):**  
   \((u^3)^3 = u^{3 \times 3} = u^9\)  

Putting it all together, the simplified expression is:

\[
-64v^6u^9
\]

This is the final answer.

Would you like more details, or do you have any other questions?

Here are five related questions you might find helpful:

1. How do you apply the power of a product rule when simplifying expressions?
2. What is the general rule for multiplying exponents when raising a power to another power?
3. How do you simplify expressions with negative bases raised to an odd power?
4. Can you explain how to simplify expressions that involve multiple variables with exponents?
5. What is the difference between simplifying and expanding an expression?

**Tip:** When raising a term with a negative base to an odd power, the result will always be negative.

Simplify (-4v^2 u^3)^3. Write your answer without parentheses.

Discover how to simplify the expression (-4v^2 u^3)^3 step-by-step using exponentiation rules. This algebra problem is perfect for students in Grades 9-10 and involves key concepts like the power of a product and the power of a power.

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