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Let's analyze and simplify the given expression:

The expression provided is:

\[
\frac{\frac{1}{v^2}}{\frac{3}{4v}}
\]

### Step-by-step simplification:

1. First, simplify the complex fraction:
   \[
   \frac{\frac{1}{v^2}}{\frac{3}{4v}} = \frac{1}{v^2} \times \frac{4v}{3}
   \]

2. Now multiply the fractions:
   \[
   = \frac{1 \times 4v}{v^2 \times 3} = \frac{4v}{3v^2}
   \]

3. Simplify the expression by canceling out the common \(v\) terms:
   \[
   \frac{4v}{3v^2} = \frac{4}{3v}
   \]

Thus, the simplified expression is:

\[
\frac{4}{3v}
\]

This is the final answer, and it uses only positive exponents.

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

Here are some follow-up questions:
1. How do you handle more complex fractions in algebra?
2. What is the general rule for simplifying fractions involving exponents?
3. How can we use the properties of exponents to simplify expressions with variables?
4. What would happen if the exponent in this case were negative?
5. How do you multiply and divide terms with exponents?

**Tip:** Always cancel out common factors in both the numerator and denominator to simplify expressions quickly.

Simplify: \frac{\frac{1}{v^2}}{\frac{3}{4v}} using only a positive exponent.

Learn how to simplify the complex algebraic expression \frac{\frac{1}{v^2}}{\frac{3}{4v}} using exponent rules. This example demonstrates multiplication of fractions and simplification using exponents, perfect for students in Grades 8-10.

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