| When simplified, \[{{(256)}^{-\,\,({{4}^{-\,3\,\,/\,2}})}}\]is [SSC (FCI) 2012] |
A) \[8\]
B) \[\frac{1}{8}\]
C) \[2\]
D) \[\frac{1}{2}\]
Correct Answer: D
Solution :
| Given, |
| \[{{(256)}^{-\,\,({{4}^{-\,\,3/2}})}}={{(256)}^{-\,\,\left( \frac{1}{{{4}^{3/2}}} \right)}}={{(256)}^{-\,\,\left( \frac{1}{{{({{2}^{2}})}^{\,3/2}}} \right)}}\] |
| \[={{(256)}^{-\frac{1}{8}}}=\frac{1}{{{(256)}^{\frac{1}{8}}}}=\frac{1}{{{({{2}^{8}})}^{1/8}}}\] |
| \[=\frac{1}{2}\] |
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