a. $\left ( \frac{8}{9} \right )^{3}.\frac{4}{3}.\frac{2}{3}$
$=\left ( \frac{8}{9} \right )^{3}.\frac{8}{9}=\left ( \frac{8}{9} \right )^{4}$
b. $\left ( \frac{1}{4} \right )^{7}.0,25$
$=(0,25)^{7}.0,25=(0,25)^{8}$
c. $(-0,125)^{6}:\frac{-1}{8}^{6}:\frac{-1}{8}$
$=\left ( \frac{-1}{8} \right )^{5}$
d. $\left [ \left ( \frac{-3}{2} \right )^{3} \right ]^{2}$
$=\left ( \frac{-3}{2} \right )^{3.2}=\left ( \frac{-3}{2} \right )^{6}$