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: C
Solution :
(c) \[\frac{{{\left( {{a}^{-n}} \right)}^{m}}\times {{a}^{-2m}}}{{{a}^{mn}}\times {{a}^{2m}}}=\frac{{{a}^{-nm}}\times {{a}^{-2m}}}{_{a}\left( mn+2m \right)}=\frac{_{a}-\left( nm+2m \right)}{_{a}\left( mn+2m \right)}\] \[={{a}^{-(mn+2m)-(mn+2m)}}={{a}^{-2(mn+2m)}}={{a}^{-2m(n+2)}}\]
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