https://file.aiquickdraw.com/mathbot/file/17254159693950d2h6vjs.jpg

Let's solve the given expression step by step.

### Expression:
\[ 4u^4 \times \left(-2v^8u^6\right) \times \left(-4v\right) \]

### Step 1: Multiply the coefficients
First, let's multiply the numerical coefficients:
\[ 4 \times (-2) \times (-4) = 4 \times (-2) = -8 \]
\[ -8 \times (-4) = 32 \]

So, the coefficient of the final expression is \( 32 \).

### Step 2: Multiply the \( u \) terms
Now, let's handle the \( u \) terms:
\[ u^4 \times u^6 \]
When multiplying like bases, we add the exponents:
\[ u^{4+6} = u^{10} \]

### Step 3: Multiply the \( v \) terms
Finally, let's deal with the \( v \) terms:
\[ v^8 \times v \]
Again, adding the exponents:
\[ v^{8+1} = v^9 \]

### Final Expression:
Combining everything, the simplified expression is:
\[ 32u^{10}v^9 \]

Would you like more details or have any questions?

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Here are 5 questions that relate to this concept:
1. How do you multiply expressions with the same base but different exponents?
2. What happens to the sign of the coefficient when you multiply two negative numbers?
3. Can you explain why the exponent rule works when multiplying like bases?
4. How would the expression change if one of the terms had a negative exponent?
5. What is the result if one of the bases has an exponent of zero?

**Tip:** Remember, when multiplying powers with the same base, always add the exponents.

Multiply the expression: 4u^4 × (-2v^8u^6) × (-4v) and simplify the answer as much as possible.

Learn how to simplify the expression 4u^4 × (-2v^8u^6) × (-4v) with a detailed step-by-step solution. This problem covers algebraic concepts such as polynomial multiplication and the product of powers rule. Suitable for students in Grades 8-10.

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