1. The problem is to simplify the expression $6a + a^{\frac{1}{2}} b^{\frac{1}{3}} - 15 b^{\frac{2}{3}}$. 2. This expression contains terms with variables $a$ and $b$ raised to fractional powers. We cannot combine terms with different variables or different powers directly. 3. The term $6a$ is a linear term in $a$. 4. The term $a^{\frac{1}{2}} b^{\frac{1}{3}}$ is a product of fractional powers of $a$ and $b$. 5. The term $-15 b^{\frac{2}{3}}$ is a term with $b$ raised to the power $\frac{2}{3}$. 6. Since none of these terms are like terms (they have different variables or powers), the expression is already simplified. Final answer: $$6a + a^{\frac{1}{2}} b^{\frac{1}{3}} - 15 b^{\frac{2}{3}}$$