(5) \( \frac{-6 a^{9}+18 a^{9}}{-\left(-2 a^{2}\right)^{4}} \)

To simplify the expression \( \frac{-6 a^{9}+18 a^{9}}{-\left(-2 a^{2}\right)^{4}} \), first combine the terms in the numerator: \[ -6 a^{9} + 18 a^{9} = 12 a^{9} \] Now let's evaluate the denominator. We have: \[ -\left(-2 a^{2}\right)^{4} = -\left(2^{4} (a^{2})^{4}\right) = -16 a^{8} \] Thus, the expression simplifies to: \[ \frac{12 a^{9}}{-16 a^{8}} = \frac{12}{-16} \cdot \frac{a^{9}}{a^{8}} = -\frac{3}{4} \cdot a = -\frac{3}{4} a \] So the final simplified answer is: \[ -\frac{3}{4} a \]