| The value of \[\sqrt[3]{{{2}^{4}}\sqrt{{{2}^{-5}}\sqrt[6]{{{2}^{6}}}}}\]is |
A) \[\sqrt[3]{4}\]
B) \[\sqrt[3]{8}\]
C) \[\sqrt[3]{2}\]
D) None of these
Correct Answer: A
Solution :
| \[\sqrt[3]{{{2}^{4}}\sqrt{{{2}^{-5}}{{\sqrt[6]{2}}^{6}}}}=\sqrt[3]{{{2}^{4}}\sqrt{{{2}^{-5}}\times 2}}\] |
| \[=\sqrt[3]{{{2}^{4}}\sqrt{{{2}^{-\,\,4}}}}=\sqrt[3]{{{2}^{4}}{{2}^{-2}}}\] |
| \[=\sqrt[3]{{{2}^{2}}}=\sqrt[3]{4}\] |
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