1. The problem asks to express the product $2^{1/5} \times 2^{2/5}$ in radical form. 2. Recall that when multiplying powers with the same base, add the exponents: $$2^{1/5} \times 2^{2/5} = 2^{(1/5 + 2/5)}$$ 3. Simplify the exponent: $$1/5 + 2/5 = 3/5$$ so the expression becomes $$2^{3/5}$$ 4. To write $2^{3/5}$ in radical form, recall that $a^{m/n} = \sqrt[n]{a^m}$. Therefore, $$2^{3/5} = \sqrt[5]{2^3}$$ 5. Simplify inside the radical: $$\sqrt[5]{8}$$ Hence, the product in radical form is $\sqrt[5]{8}$.