| The value of\[{{\left( \frac{1}{64} \right)}^{0}}+{{(64)}^{-1/2}}+{{(32)}^{4/5}}-{{(32)}^{-\,\,4/5}}\]is |
A) \[17\frac{1}{15}\]
B) \[15\frac{1}{17}\]
C) \[10\frac{1}{17}\]
D) \[17\frac{1}{16}\]
Correct Answer: D
Solution :
| Given, \[{{\left( \frac{1}{64} \right)}^{0}}+{{(64)}^{-\,\,1/2}}+{{(32)}^{4/5}}-{{(32)}^{-\,\,4/5}}\] |
| \[=1+{{\left( \frac{1}{64} \right)}^{1/2}}+{{(32)}^{4/5}}-{{\left( \frac{1}{32} \right)}^{4/5}}\] |
| \[\left[ \because {{a}^{0}}=1,{{a}^{-m}}=\frac{1}{{{a}^{m}}} \right]\] |
| \[=1+{{\left( \frac{1}{{{8}^{2}}} \right)}^{1/2}}+{{(2)}^{5\times \frac{4}{5}}}-\frac{1}{{{(2)}^{5\times \frac{4}{5}}}}\] |
| \[=1+\frac{1}{8}+{{(2)}^{4}}-\frac{1}{{{(2)}^{4}}}\] |
| \[=\frac{1}{8}+16-\frac{1}{16}=17\frac{1}{16}\] |
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