Simplify: |
(a) \[\frac{{{12}^{4}}\times {{9}^{3}}\times 4}{{{6}^{3}}\times {{8}^{2}}\times 27}\] |
(b) \[{{2}^{3}}\times {{a}^{3}}\times 5{{a}^{4}}\] |
Answer:
(a) \[\frac{{{12}^{4}}\times {{9}^{3}}\times 4}{{{6}^{3}}\times {{8}^{2}}\times 27}=\frac{\left( 3\times {{2}^{2}} \right)4\times {{\left( {{3}^{2}} \right)}^{3}}\times {{2}^{2}}}{{{\left( 2\times 3 \right)}^{3}}\times {{\left( {{2}^{3}} \right)}^{2}}\times {{3}^{3}}}\] =\[\frac{{{3}^{4}}\times {{2}^{8}}\times {{3}^{6}}\times {{2}^{2}}}{{{2}^{3}}\times {{3}^{3}}\times {{2}^{6}}\times {{3}^{3}}}\] =\[\frac{{{2}^{8+2}}\times {{3}^{6+4}}}{{{2}^{6+3}}\times {{3}^{3+3}}}\] =\[\frac{{{2}^{10}}\times {{3}^{10}}}{{{2}^{9}}\times {{3}^{6}}}={{2}^{10-9}}\times {{3}^{10-6}}\] \[=2\times {{3}^{4}}=2\times 81=162\] (b) \[{{2}^{3}}\times {{a}^{3}}\times 5{{a}^{4}}\] \[=8\times {{a}^{3}}\times 5\times {{a}^{4}}\] \[=8\times 5\times {{a}^{3}}\times {{a}^{4}}\] \[=40\times {{a}^{3+4}}\] \[=40\times {{a}^{7}}\] \[=40\times {{a}^{7}}\] \[=40{{a}^{7}}\]
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