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To simplify the given expression:

\[
v^{-3} \cdot 8 \cdot x^9
\]

### Steps to simplify:
1. **Break down the components**: 
   - \( v^{-3} \) means \( \frac{1}{v^3} \) (move it to the denominator to make the exponent positive).
   - \( 8 \) remains as a constant in the numerator.
   - \( x^9 \) stays in the numerator as it already has a positive exponent.

2. **Combine into a single fraction**:
   - Numerator: \( 8x^9 \)
   - Denominator: \( v^3 \)

Thus, the simplified expression is:

\[
\frac{8x^9}{v^3}
\]

Let me know if you need a more detailed explanation!  

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### Related Questions:
1. How do you simplify expressions with negative exponents?
2. What is the rule for multiplying powers of the same base?
3. How do you move terms with negative exponents to the denominator or numerator?
4. What is the difference between a positive and negative exponent?
5. How do you simplify \( (x^a)(x^b) \) when combining like terms?

### Tip:
When simplifying expressions with exponents, remember that **negative exponents** mean the reciprocal of the base raised to the positive exponent. Always rewrite terms carefully!

Simplify the following expression: v^(-3) * 8 * x^9

Learn how to simplify the expression v^(-3) * 8 * x^9 by applying exponent rules. This step-by-step solution demonstrates handling negative exponents, rewriting terms, and combining results into a fraction. Ideal for Grades 8-10 students studying exponents and algebra.

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