question_answer

Simplify: \[{{\left[ {{\left( 2\div 1 \right)}^{-1}}\div {{\left( 5\div 1 \right)}^{-1}} \right]}^{2}}\times {{\left( \frac{-5}{8} \right)}^{-1}}\]

Answer:

\[{{[{{(2\div l)}^{-l}}\div {{(5\div l)}^{-l}}]}^{2}}\times {{\left( \frac{-5}{8} \right)}^{-1}}\] =\[{{\left( \frac{1}{2}\div \frac{1}{5} \right)}^{2}}\times \left( \frac{8}{-5} \right)\] \[={{\left( \frac{1}{2}\times 5 \right)}^{2}}\times \left( \frac{2\times 2\times 2}{-5} \right)\]                                                                                                 \[=\frac{1}{{{2}^{2}}}\times {{5}^{2}}\times \frac{{{2}^{3}}}{-5}\] \[={{2}^{3-2}}\times {{5}^{2-1}}\] \[=2\times 5\] = - 10.