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To simplify the given expression \( \frac{2v^4 \cdot v^{-9} \cdot 5x^8 \cdot y^{-8} \cdot 5x^8 \cdot y^{-6}}{} \), let's break it down step-by-step:

### Step 1: Combine like terms for \(v\):
\[
v^4 \cdot v^{-9} = v^{4 + (-9)} = v^{-5}
\]

### Step 2: Combine like terms for \(x\):
\[
5x^8 \cdot 5x^8 = (5 \cdot 5) \cdot x^{8 + 8} = 25x^{16}
\]

### Step 3: Combine like terms for \(y\):
\[
y^{-8} \cdot y^{-6} = y^{(-8) + (-6)} = y^{-14}
\]

### Step 4: Putting it all together:
The simplified expression is:
\[
25x^{16} v^{-5} y^{-14}
\]

### Step 5: Convert to only positive exponents:
- \(v^{-5}\) becomes \( \frac{1}{v^5} \)
- \(y^{-14}\) becomes \( \frac{1}{y^{14}} \)

Thus, the final simplified expression is:
\[
\frac{25x^{16}}{v^5 y^{14}}
\]

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Would you like further details on any part of this simplification?

Here are some related questions to deepen your understanding:
1. How do you handle negative exponents in more complex expressions?
2. What are the rules for multiplying terms with the same base?
3. How can you simplify expressions with fractional exponents?
4. What is the difference between simplifying and factoring expressions?
5. How do you handle expressions that involve both addition and multiplication of exponents?

**Tip:** When simplifying expressions, always combine like terms first to make the expression easier to manage!

Simplify: 2v^4 · v^-9 · 5x^8 · y^-8 · 5x^8 · y^-6 using only positive exponents.

Learn how to simplify the expression 2v^4 · v^-9 · 5x^8 · y^-8 · 5x^8 · y^-6 by combining like terms and converting to positive exponents. This problem involves key algebraic concepts, such as exponent rules and simplification. Suitable for students in Grades 8-10.

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