a) \( \frac{3^{\frac{2}{5}} \cdot 3^{-\frac{4}{5}}}{3^{\frac{8}{5}}} \)

First, let's simplify the expression using the properties of exponents. We can combine the exponents in the numerator: \[ 3^{\frac{2}{5}} \cdot 3^{-\frac{4}{5}} = 3^{\frac{2}{5} - \frac{4}{5}} = 3^{-\frac{2}{5}} \] Now, substituting this back into the expression gives us: \[ \frac{3^{-\frac{2}{5}}}{3^{\frac{8}{5}}} \] Next, we apply the quotient rule, which states that when dividing powers with the same base, we subtract the exponents: \[ 3^{-\frac{2}{5} - \frac{8}{5}} = 3^{-\frac{10}{5}} = 3^{-2} \] Finally, we can express \(3^{-2}\) as a fraction: \[ 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \] So, the final answer is: \[ \frac{1}{9} \]