question_answer 4)

                Evaluate:                 (i) \[\frac{{{8}^{-1}}\times {{5}^{3}}}{{{2}^{-4}}}\]                             (ii) \[({{5}^{-1}}\times {{2}^{-1}})\,\times {{6}^{-1}}\]

Answer:

                (i) \[\frac{{{8}^{-1}}\times {{5}^{3}}}{{{2}^{-4}}}\]                                             \[=\frac{\frac{1}{{{8}^{1}}}\times 125}{\frac{1}{{{2}^{4}}}}\] \[=\frac{\frac{1}{8}\,\times 125}{\frac{1}{16}}\] \[=\frac{1}{8}\times 125\,\times \frac{16}{1}\] \[=250\] (ii) \[({{5}^{-1}}\times {{2}^{-1}})\,\times {{6}^{-1}}\] \[({{5}^{-1}}\times {{2}^{-1}})\,\times {{6}^{-1}}\]\[=\left( \frac{1}{5}\,\times \frac{1}{2} \right)\,\times \frac{1}{6}\] \[=\frac{1}{10}\,\times \frac{1}{6}\,=\frac{1}{60}\]