1. **State the problem:** Simplify the expression $$\frac{a^{2/3}}{b^{1/3}} + \frac{b^{2/3}}{a^{1/3}}$$ and find which given option it is equivalent to. 2. **Rewrite the expression:** Use the property of exponents $$\frac{x^m}{y^n} = x^m y^{-n}$$ to write each term: $$\frac{a^{2/3}}{b^{1/3}} = a^{2/3} b^{-1/3}$$ $$\frac{b^{2/3}}{a^{1/3}} = b^{2/3} a^{-1/3}$$ 3. **Find a common denominator:** To combine the terms, multiply numerator and denominator appropriately: $$\frac{a^{2/3} b^{-1/3} \cdot a^{1/3} b^{1/3}}{a^{1/3} b^{1/3}} + \frac{b^{2/3} a^{-1/3} \cdot a^{1/3} b^{1/3}}{a^{1/3} b^{1/3}}$$ 4. **Simplify numerator terms:** $$a^{2/3 + 1/3} b^{-1/3 + 1/3} + b^{2/3 + 1/3} a^{-1/3 + 1/3} = a^{1} b^{0} + b^{1} a^{0} = a + b$$ 5. **Write the combined expression:** $$\frac{a + b}{a^{1/3} b^{1/3}}$$ 6. **Conclusion:** The expression is equivalent to option A. **Final answer:** $$\frac{a + b}{a^{1/3} b^{1/3}}$$