Simplify. \[ \frac{v^{\frac{4}{9}}}{v^{\frac{2}{3}}} \] Write your answer using only a positive exponent. Assume that the variable represents a positive real number.

Step 1 ：We are given the expression \(\frac{v^{\frac{4}{9}}}{v^{\frac{2}{3}}}\).

Step 2 ：We can simplify this expression by subtracting the exponent of the denominator from the exponent of the numerator, as they have the same base.

Step 3 ：This gives us the expression \(v^{-0.222222222222222}\).

Step 4 ：However, the question asks for the answer with only a positive exponent. We can achieve this by taking the reciprocal of the expression, which will change the sign of the exponent.

Step 5 ：This gives us the final expression \(v^{0.222222222222222}\).

Step 6 ：Final Answer: The simplified expression with a positive exponent is \(\boxed{v^{0.222222222222222}}\).