https://file.aiquickdraw.com/mathbot/file/1725118913391s9e1a9g5.jpg

The expression given in the image is:

\[
3w^7v^6 \cdot (-6w) \cdot 2v^4
\]

To multiply these expressions together, follow these steps:

1. **Multiply the coefficients**: \( 3 \times (-6) \times 2 = -36 \).

2. **Multiply the powers of \( w \)**:
   - \( w^7 \) and \( w^1 \) (since \( -6w \) is the same as \( -6w^1 \)):
   \[
   w^7 \times w^1 = w^{7+1} = w^8
   \]

3. **Multiply the powers of \( v \)**:
   - \( v^6 \) and \( v^4 \):
   \[
   v^6 \times v^4 = v^{6+4} = v^{10}
   \]

Putting it all together, the product is:

\[
-36w^8v^{10}
\]

Would you like more details or have any questions? 

Here are some related questions for further practice:

1. How would you simplify \( 2x^3y^2 \times 5x^4y \times 3y^3 \)?
2. What happens if the base variables \( w \) or \( v \) have different bases?
3. How do you handle multiplication when variables have negative exponents?
4. Can you explain the laws of exponents used in simplifying the expression?
5. What would be the result if one of the terms was \( w^{-2} \) instead of \( w^1 \)?

**Tip:** Always combine like terms by adding the exponents when multiplying expressions with the same base.

Understand how to multiply algebraic expressions like -36w^8v^10 with a step-by-step solution. This problem covers multiplication of coefficients and powers of variables, demonstrating exponent rules. Suitable for students in Grades 7-9.

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