A) \[\frac{-b{{c}^{3}}}{{{a}^{2}}}\]
B) \[\frac{b{{c}^{4}}}{{{a}^{2}}}\]
C) \[\frac{-a{{b}^{4}}}{{{c}^{2}}}\]
D) \[\frac{-b{{c}^{4}}}{{{a}^{2}}}\]
Correct Answer: D
Solution :
We have, \[\sqrt[3]{\frac{-{{a}^{6}}\times {{b}^{3}}\times {{c}^{21}}}{{{c}^{9}}\times {{a}^{12}}}}=\sqrt[3]{\frac{-{{b}^{3}}\times {{c}^{12}}}{{{a}^{6}}}}\] \[={{\left( \frac{(-b)\times (-b)\times (-b)\times {{c}^{4}}\times {{c}^{4}}\times {{c}^{4}}}{{{a}^{2}}\times {{a}^{2}}\times {{a}^{2}}} \right)}^{\frac{1}{3}}}\] \[={{\left( \frac{-b\times {{c}^{4}}}{{{a}^{2}}} \right)}^{3\times \frac{1}{3}}}=\frac{-b{{c}^{4}}}{{{a}^{2}}}\]
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