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The given expression is:

\[
2u \cdot v^5 \cdot 7uv^8
\]

Let's simplify it step by step:

1. Multiply the constants: \(2 \times 7 = 14\).
2. Combine the \(u\) terms: \(u \cdot u = u^2\).
3. Combine the \(v\) terms: \(v^5 \cdot v^8 = v^{5+8} = v^{13}\).

Now the simplified expression is:

\[
14u^2v^{13}
\]

Let me know if you have any questions or need further details!

Here are 5 related questions you might consider:
1. How do you multiply terms with the same base but different exponents?
2. What happens when you multiply powers with the same base?
3. Can you explain how to simplify expressions involving variables and exponents?
4. What does it mean to express an answer using only positive exponents?
5. How do you distribute multiplication over multiple variables in algebra?

**Tip:** When multiplying variables with exponents, always add the exponents if the bases are the same.

Simplify the expression 2u * v^5 * 7uv^8. Express your answer using positive exponents.

Learn how to simplify the expression 2u * v^5 * 7uv^8 using exponent rules. This algebraic problem covers multiplying variables with exponents and the product rule for exponents. Suitable for students in Grades 7-9.

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