1. **State the problem:** Simplify the expression $\frac{2}{\sqrt[5]{2}}$. 2. **Recall the rule:** The $n$th root of a number can be written as a fractional exponent: $\sqrt[n]{a} = a^{\frac{1}{n}}$. 3. **Rewrite the denominator:** $\sqrt[5]{2} = 2^{\frac{1}{5}}$. 4. **Rewrite the expression:** $\frac{2}{2^{\frac{1}{5}}}$. 5. **Use the property of exponents:** $\frac{a^m}{a^n} = a^{m-n}$. 6. **Apply the property:** $2^{1 - \frac{1}{5}} = 2^{\frac{5}{5} - \frac{1}{5}} = 2^{\frac{4}{5}}$. 7. **Final answer:** $2^{\frac{4}{5}}$. This is the simplified form of the original expression.