(-3a^{1/4})(9a)^{-3/2}
If you understood the properties, I suspect you would not be having difficulties with the problem. By the way, we have nothing to "solve" here, this is not an equation. Rather, we are "simplifying" the expression.
$\displaystyle \left(-3a^{1/4}\right)(9a)^{-3/2}$
$\displaystyle =-3a^{1/4}\cdot9^{-3/2}a^{-3/2}$
$\displaystyle =-\frac{3a^{1/4}}{9^{3/2}a^{3/2}}$
$\displaystyle =-\frac{3a^{1/4}}{27a^{3/2}}$
Now, use the properties $\displaystyle \frac{a^m}{a^n} = a^{m-n}$ and $\displaystyle a^{-n} = \frac1{a^n}$ to finish it:
$\displaystyle =-\frac{a^{-5/4}}{9}=-\frac1{9a^{5/4}}$
As a final step, you may want to convert $\displaystyle a^{5/4}$ to radical form, depending on the problem's instructions.