A) 6
B) 9
C) 8
D) None of these
Correct Answer: D
Solution :
\[{{(216)}^{3/5}}={{({{6}^{3}})}^{3/5}}={{6}^{9/5}}\] \[={{(2\times 3)}^{9/5}}={{2}^{9/5}}\times {{3}^{9/5}}\] \[{{(2500)}^{\frac{2}{5}}}={{(50)}^{2\times \frac{2}{5}}}={{(50)}^{\frac{4}{5}}}\] \[={{({{5}^{2}}\times 2)}^{\frac{4}{5}}}={{5}^{8/5}}\times {{2}^{4/5}}\] \[{{(300)}^{\frac{1}{5}}}={{(3\times {{10}^{2}})}^{\frac{1}{5}}}={{3}^{\frac{1}{5}}}\times {{2}^{\frac{2}{5}}}\times {{5}^{\frac{2}{5}}}\] \[\therefore {{(216)}^{\frac{3}{5}}}\times {{(2500)}^{\frac{2}{5}}}\times {{(300)}^{\frac{1}{5}}}\] \[={{2}^{\frac{9}{5}}}\times {{3}^{\frac{9}{5}}}\times {{5}^{\frac{8}{5}}}\times {{2}^{\frac{4}{5}}}\times {{3}^{\frac{1}{5}}}\times {{2}^{\frac{2}{5}}}\times {{5}^{\frac{2}{5}}}\] \[={{2}^{15/5}}\times {{3}^{10/5}}\times {{5}^{10/5}}={{2}^{3}}\times {{3}^{2}}\times {{5}^{2}}\]
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