a) $1\frac{3}{4} \times \frac{-16}{7} = \frac{7}{4} \times \frac{-16}{7} = -4$;
b) $12 / \frac{-6}{5} + \frac{1}{5} = 12 \times \frac{-5}{6} + \frac{1}{5} = -10 + 0.2 = -9.8;$
c) $\frac{2}{9} + \frac{1}{3} / (-\frac{3}{2}) + \frac{1}{2} \times (-0.5) = \frac{2}{9} + \frac{1}{3} \times (-\frac{2}{3}) + \frac{1}{2} \times \frac{-1}{2} = \frac{2}{9} + \frac{-2}{9} + \frac{-1}{4} = \frac{-1}{4};$
d) $(0.1)^{21} / (-0.01)^{10} = (0.1)^{21} / (0.01)^{10} = (0.1)^{21} / [(0.1)^{2}]^{10} = (0.1)^{21} / (0.1)^{20} = 0.1$