A) \[{{2}^{32/31}}\]
B) \[{{2}^{0}}\]
C) \[{{2}^{31/32}}\]
D) \[{{2}^{30/32}}\]
Correct Answer: C
Solution :
Expression \[=\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}}\] \[=\sqrt{2\sqrt{2\sqrt{2\sqrt{2\times {{2}^{1/2}}}}}}\] \[=\sqrt{2\sqrt{2\sqrt{2\times {{2}^{3/4}}}}}\] \[=\sqrt{2\sqrt{2\sqrt{{{2}^{7/4}}}}}=\sqrt{2\sqrt{2\sqrt{{{2}^{7/8}}}}}\] \[=\sqrt{2\times {{2}^{15/16}}}=\sqrt{{{2}^{31/16}}}={{2}^{31/32}}\]
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