| \[\sqrt[3]{{{(64)}^{-1/6}}\times {{(81)}^{3/4}}\times {{(64)}^{2/3}}}\]is [SSC (CGL) 2014] |
A) 6
B) 2
C) 12
D) 24
Correct Answer: A
Solution :
| \[=\sqrt[3]{{{(64)}^{-1/6}}\times {{(81)}^{3/4}}\times {{(64)}^{2/3}}}\] |
| \[=\sqrt[3]{{{({{2}^{6}})}^{-1/6}}\times {{({{3}^{4}})}^{3/4}}\times {{({{4}^{3}})}^{2/3}}}\] |
| \[=\sqrt[3]{{{({{2}^{6}})}^{\frac{-1}{6}}}\times {{(3)}^{4\,\,\times \,\,\frac{3}{4}}}\times {{(4)}^{3\,\,\times \,\,\frac{2}{3}}}}\] |
| \[=\sqrt[3]{\frac{1}{2}\times {{3}^{3}}\times {{4}^{2}}}=\sqrt[3]{{{3}^{3}}\times \frac{4\times 4}{2}}\] |
| \[=\sqrt[3]{{{3}^{3}}\times {{2}^{3}}}=3\times 2=6\] |
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