A) 16
B) 8
C) 4
D) \[\frac{1}{8}\]
Correct Answer: D
Solution :
(d) \[{{\left( 4096 \right)}^{\frac{-1}{4}}}={{\left( {{2}^{12}} \right)}^{-1/4}}={{2}^{\left( 12\times \frac{-1}{4} \right)}}={{2}^{-3}}=\frac{1}{8}\] Mathematical ingenuity: It is worthwhile to remember a few powers of 2 and 3: e.g., \[{{2}^{2}}=4;{{........2}^{6}}={{6}^{4}}{{..........2}^{10}}=1024\] Similarly \[{{3}^{2}}=9;\] \[{{3}^{3}}=27....;{{....3}^{5}}=243,\,\,{{3}^{6}}=729\] etc.
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