(a) \( a^{\frac{1}{3}}\left(a^{\frac{5}{3}}-a^{\frac{-2}{3}}\right) \)

First, let's simplify the expression \( a^{\frac{1}{3}}(a^{\frac{5}{3}} - a^{-\frac{2}{3}}) \). We start by distributing \( a^{\frac{1}{3}} \): \[ a^{\frac{1}{3}} \cdot a^{\frac{5}{3}} - a^{\frac{1}{3}} \cdot a^{-\frac{2}{3}}. \] Using the exponent addition rule \( a^m \cdot a^n = a^{m+n} \): 1. The first part becomes: \[ a^{\frac{1}{3} + \frac{5}{3}} = a^{\frac{6}{3}} = a^2. \] 2. The second part simplifies to: \[ a^{\frac{1}{3} - \frac{2}{3}} = a^{-\frac{1}{3}}. \] Putting it all together, we have: \[ a^2 - a^{-\frac{1}{3}}. \] To express that in a different form, we can write \( a^{-\frac{1}{3}} \) as \( \frac{1}{a^{\frac{1}{3}}} \): Thus, the final simplified expression is: \[ a^2 - \frac{1}{a^{\frac{1}{3}}}. \]