[tex]1) \: \: \: \: \: {( \frac{1}{3}) }^{ - 2} - {( - 2)}^{ - 3} = {3}^{2} - {( - \frac{1}{2}) }^{3} = 9 - ( - \frac{1}{8} ) = 9 + \frac{1}{8} = 9 \frac{1}{8} [/tex]

[tex]2) \: \: \: \: \: {( - 3)}^{ - 3} - {( \frac{1}{2} )}^{ - 4} = {( - \frac{1}{3} )}^{3} - {2}^{4} = - \frac{1}{27} - 16 = - 16 \frac{1}{27} [/tex]

[tex]3) \: \: \: \: \: {( - 10)}^{ - 3} + {( \frac{2}{3}) }^{ - 2} = {( - 10)}^{3} + {( \frac{2}{3}) }^{2} = - 1000 + \frac{4}{9} = - 999 \frac{5}{9} [/tex]

[tex]4) \: \: \: \: \: {( \frac{2}{7} )}^{ - 3} + {( - 2)}^{ - 5} = { (\frac{7}{2}) }^{3} + {( - \frac{1}{2} )}^{5} = \frac{343}{8} - \frac{1}{32} = \frac{1372 - 1}{32} = \frac{1371}{32} = 42 \frac{27}{32} [/tex]