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