A) \[100\,{{a}^{\frac{25}{4}}}\]
B) \[\frac{1}{100{{a}^{\frac{21}{4}}}}\]
C) \[20{{a}^{\frac{-21}{4}}}\]
D) \[20\,{{a}^{\frac{21}{4}}}\]
Correct Answer: B
Solution :
(b) \[\frac{{{\left( 9{{a}^{2}} \right)}^{\frac{1}{2}}}\times {{\left( 25{{a}^{4}} \right)}^{-1/2}}}{5\times 3\times 4\times {{a}^{\frac{1}{2}+\frac{3}{2}+\frac{9}{4}}}}\] \[=\frac{{{\left( {{3}^{2}}{{a}^{2}} \right)}^{\frac{1}{2}}}\times {{\left( {{5}^{2}}{{a}^{4}} \right)}^{\frac{-1}{2}}}}{60{{a}^{17/4}}}=\frac{3a\times {{5}^{-1}}{{a}^{-2}}}{60{{a}^{17/4}}}\] \[=\frac{3{{a}^{-1}}}{5\times 60\times {{a}^{17/4}}}\] \[=\frac{{{a}^{\frac{-21}{4}}}}{100}\] \[=\frac{1}{100{{a}^{\frac{21}{4}}}}\]
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