Let's simplify the expression \((-24x^3)(-4y^2z)(-3xyz)\).

### Step-by-step solution:
1. **Multiply the coefficients**:  
   \((-24) \times (-4) \times (-3)\)  
   \[ = -24 \times -4 = 96 \]  
   \[ 96 \times -3 = -288 \]

2. **Multiply the variables**:
   - For \(x\), we have \(x^3 \times x \times x = x^{3+1+1} = x^5\).
   - For \(y\), we have \(y^2 \times y = y^{2+1} = y^3\).
   - For \(z\), we have \(z \times z = z^2\).

### Final expression:
\[
(-24x^3)(-4y^2z)(-3xyz) = -288x^5y^3z^2
\]

Would you like more details or have any questions?

### Related Questions:
1. What happens if we change one of the exponents in the expression?
2. How would the result change if one of the terms had a negative exponent?
3. What are the rules for multiplying powers with the same base?
4. Can you explain how to handle exponents when dividing terms instead of multiplying?
5. How does the final expression compare if we were working with addition instead of multiplication?

**Tip**: When multiplying powers with the same base, add their exponents.

Explore the step-by-step solution to simplifying the polynomial expression (-24x^3)(-4y^2z)(-3xyz). Learn how to multiply coefficients and add exponents for terms with the same base. This guide is ideal for high school students in Grades 9-10, covering key concepts like exponent rules and polynomial multiplication.

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