| The value of\[\frac{1}{{{(216)}^{-\,\,2/3}}}+\frac{1}{{{(256)}^{-\,\,3/4}}}+\frac{1}{{{(32)}^{-\,\,1/5}}}\]is |
A) 102
B) 105
C) 107
D) 109
Correct Answer: A
Solution :
| \[\frac{1}{{{(216)}^{-\,\,2/3}}}+\frac{1}{{{(256)}^{-\,\,3/4}}}+\frac{1}{{{(32)}^{-\,\,1/5}}}\] |
| \[\Rightarrow \] \[\frac{1}{{{(6)}^{3\,\,\times \,\,-\,\,\frac{2}{3}}}}+\frac{1}{{{(4)}^{4\,\,\times \,\,-\,\,\frac{3}{4}}}}+\frac{1}{{{(2)}^{5\,\,\times \,\,-\,\,\frac{1}{5}}}}\] |
| \[\frac{1}{{{(6)}^{-\,\,2}}}+\frac{1}{{{(4)}^{-\,\,3}}}+\frac{1}{{{(2)}^{-\,\,1}}}\] |
| \[\Rightarrow \] \[36+64+2=102\] |
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