question_answer

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) \[{{2}^{3}}\times {{a}^{3}}\times 5{{a}^{4}}\]

\[=8\times {{a}^{3}}\times 5\times {{a}^{4}}\]

\[=8\times 5\times {{a}^{3}}\times {{a}^{4}}\]

\[=40\times {{a}^{3+4}}\]

\[=40\times {{a}^{7}}\]

\[=40\times {{a}^{7}}\]

\[=40{{a}^{7}}\]