a) $\frac{6^{2} . 6^{3}}{3^{5}}$ = $\frac{6^{5}}{3^{5}}$ = $(\frac{6}{3})^{5}$ = 2$^{5}$ = 32;           

b) $\frac{25^{2} . 4^{2}}{5^{5} . (-2)^{5}}$ = $\frac{(25.4)^{2}}{(5.(-2)^{5}}$ = $\frac{(100)^{2}}{(-10)^{5}}$ = $\frac{(10)^{4}}{(-10)^{5}}$ = $\frac{-1}{10}$;             

c) $\frac{0,125^{5} . (2,4)^{5}}{(-0,3)^{5} . (0,01)^{3}}$ = $\frac{0,125^{5} . (2,4)^{5}}{(-0,3)^{5} . (0,01)^{3}}$ = $\frac{(0,125 . 2,4)^{5}}{(-0,3)^{5} . (0,01)^{3}}$ = $\frac{(0,3)^{5}}{(-0,3)^{5} . (0,01)^{3}}$ = $\frac{1}{-(0,01)^{3}}$ = -1000000;

d) $(-2\frac{3}{4} + \frac{1}{2})^{2}$ = $(-\frac{11}{4} + \frac{1}{2})^{2}$ = $(-\frac{11}{4} + \frac{2}{4})^{2}$ = $(\frac{-9}{4})^{2}$ = $\frac{81}{16}$.