A) \[\frac{9}{10}{{a}^{2}}b{{c}^{4}}\]
B) \[\frac{1}{10}{{a}^{4}}{{b}^{4}}{{c}^{10}}\]
C) \[\frac{3}{10}{{a}^{4}}{{b}^{10}}{{c}^{4}}\]
D) \[\frac{3}{10}a{{b}^{4}}{{c}^{3}}\]
Correct Answer: C
Solution :
[c] \[\left( \frac{3}{15}{{a}^{5}}{{b}^{6}}{{c}^{3}}\times \frac{5}{9}a\,{{b}^{5}}{{c}^{4}} \right)\div \frac{10}{27}{{a}^{2}}b\,{{c}^{3}}\] \[=\frac{1}{9}{{a}^{6}}{{b}^{11}}{{c}^{7}}\div \frac{10}{27}{{a}^{2}}b\,{{c}^{3}}\] \[=\frac{1}{9}{{a}^{6}}{{b}^{11}}{{c}^{7}}\times \frac{27}{10}{{a}^{-\,2}}{{b}^{-\,1}}{{c}^{-\,3}}=\frac{3}{10}{{a}^{6-\,2}}{{b}^{11-\,1}}{{c}^{7-\,3}}\] \[=\frac{3}{10}{{a}^{4}}{{b}^{10}}{{c}^{4}}\]
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