| The value of \[{{(64)}^{\frac{1}{6}}}\times {{\left( \frac{3}{2} \right)}^{4}}\div {{(121)}^{0}}+{{\left( \frac{1}{3} \right)}^{4}},\]is equal to |
A) \[24\]
B) \[32\]
C) \[\frac{161}{648}\]
D) \[\frac{6569}{648}\]
Correct Answer: D
Solution :
| \[{{(64)}^{\frac{1}{6}}}\times {{\left( \frac{3}{2} \right)}^{4}}\div {{(121)}^{0}}+{{\left( \frac{1}{3} \right)}^{4}}\] |
| \[={{(2)}^{6\times \frac{1}{6}}}\times \frac{81}{16}\times \frac{1}{1}+{{\left( \frac{1}{3} \right)}^{4}}\] |
| \[=(2)\times \frac{81}{16}\times 1+\frac{1}{81}\] |
| \[=\frac{81}{8}+\frac{1}{81}\] |
| \[\Rightarrow \]\[\frac{{{(81)}^{2}}+8}{648}=\frac{6561+8}{648}=\frac{6569}{648}\] |
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