A) 32
B) 8
C) 1
D) 0
Correct Answer: D
Solution :
Given expression \[=\left[ 8-{{\left( \frac{{{4}^{\frac{9}{4}}}\sqrt{2\times {{2}^{2}}}}{2\sqrt{{{2}^{{{-}^{2}}}}}} \right)}^{\frac{1}{2}}} \right]\] \[=\left[ 8-{{\left( \frac{{{2}^{2\times \frac{9}{4}}}\times {{2}^{\frac{3}{2}}}}{2\times {{({{2}^{-2}})}^{\frac{1}{2}}}} \right)}^{\frac{1}{2}}} \right]=\left[ 8-{{\left( \frac{{{2}^{\frac{9}{2}}}\times {{2}^{\frac{3}{2}}}}{{{2}^{1}}\times {{2}^{-1}}} \right)}^{\frac{1}{2}}} \right]=\left[ 8-{{\left( \frac{{{2}^{\frac{9}{2}+\frac{3}{2}}}}{{{2}^{1-1}}} \right)}^{\frac{1}{2}}} \right]\]\[=\left[ 8-{{({{2}^{6}})}^{\frac{1}{2}}} \right]=(8-{{2}^{3}})=8-8=0\]
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