| Value of the expression \[{{\left[ \frac{{{(\sqrt{4})}^{5}}\times {{(\sqrt{4})}^{-\,\,3}}}{{{(\sqrt{4})}^{-\,\,2}}} \right]}^{\frac{3}{2}}}\]is |
A) \[{{2}^{6}}\]
B) \[{{2}^{2}}\]
C) \[{{2}^{8}}\]
D) \[{{2}^{4}}\]
Correct Answer: A
Solution :
| \[{{\left[ \frac{{{(\sqrt{4})}^{5}}\times {{(\sqrt{4})}^{-\,\,3}}}{{{(\sqrt{4})}^{-\,\,2}}} \right]}^{3/2}}\] |
| \[={{\left[ \frac{{{2}^{5}}\times {{2}^{-\,\,3}}}{{{2}^{-\,\,2}}} \right]}^{3/2}}={{\left( \frac{{{2}^{2}}}{{{2}^{-\,\,2}}} \right)}^{3/2}}\] |
| \[={{({{2}^{2\,\,+\,\,2}})}^{3/2}}={{({{2}^{4}})}^{3/2}}={{2}^{6}}\] |
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