1. The problem asks to express the fifth root of $n^4$ using rational exponents. 2. Recall the rule for radicals and exponents: $$\sqrt[b]{a^c} = a^{\frac{c}{b}}$$ where $b$ is the root and $c$ is the power inside the root. 3. Applying this rule to $\sqrt[5]{n^4}$, we get: $$\sqrt[5]{n^4} = n^{\frac{4}{5}}$$ 4. This means the fifth root of $n^4$ is the same as $n$ raised to the power of $\frac{4}{5}$. 5. Therefore, the correct answer is option A: $n^{\frac{4}{5}}$.