[tex]a) \frac{1000 \times ( - 10 {)}^{8} }{ {10}^{9} } = \frac{ {10}^{3} \times {10}^{8} }{ {10}^{9} } = \frac{ {10}^{11} }{ {10}^{9} } = {10}^{2} [/tex]
[tex]b)81 \times ( - 3 {)}^{5} \times ( - 27) = {3}^{4} \times ( - 3 {)}^{5} \times ( - 3 {)}^{3} = {3}^{4} \times ( - 3 {)}^{8} = {3}^{4} \times {3}^{8} = {3}^{12} [/tex]
[tex]c) ( - \frac{1}{32} ) \times \frac{1}{16} \times ( \frac{1}{2} {)}^{6} = ( - \frac{1}{2} {)}^{5} \times ( \frac{1}{2} {)}^{4} \times ( \frac{1}{2} {)}^{6} = ( - 2 {)}^{ - 5} \times 2 {}^{ - 4} \times {2}^{ - 6} = { - 2}^{ - 15} [/tex]
[tex]d) \frac{36 \times ( - 6 {)}^{7} \times ( - 6 {)}^{8} }{ {6}^{14} \div ( - 6) } = \frac{ {6}^{2} \times ( - 6 {)}^{7} \times {6}^{8} }{ {6}^{14} \div ( - 6) } = \frac{ {6}^{2} \times {6}^{7} \times {6}^{8} }{ {6}^{14} \div 6} = \frac{ {6}^{17} }{ {6}^{13} } = {6}^{4} [/tex]
