A) \[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{10}}} \right]}^{1/3}}\]
B) \[\frac{1}{5}{{\left[ \frac{n}{{{m}^{2}}{{6}^{10}}} \right]}^{1/3}}\]
C) \[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{-10}}} \right]}^{1/3}}\]
D) \[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{10}}} \right]}^{2/3}}\]
Correct Answer: A
Solution :
\[\frac{{{(9\,{{m}^{2}})}^{\frac{1}{3}}}}{{{6}^{4}}}\times \frac{{{(4\,{{n}^{2}})}^{\frac{1}{3}}}}{5\,m}\]\[=\frac{{{6}^{\frac{-10}{3}}}\,{{m}^{\frac{-1}{3}}}{{n}^{\frac{2}{3}}}}{5}=\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{10}}} \right]}^{\frac{1}{3}}}\]
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