A) \[{{5}^{2}}\]
B) \[{{5}^{4}}\]
C) \[{{5}^{8}}\]
D) \[{{5}^{12}}\]
Correct Answer: B
Solution :
\[{{\left[ \sqrt[2]{\sqrt[6]{{{5}^{9}}}} \right]}^{4}}{{\left[ \sqrt[6]{\sqrt[3]{{{5}^{9}}}} \right]}^{4}}\] \[={{\left[ {{5}^{9\times \frac{1}{6}\times \frac{1}{3}}} \right]}^{-4}}{{\left[ {{5}^{9\times \frac{1}{6}\times \frac{1}{3}}} \right]}^{4}}\] \[=\left[ {{5}^{\frac{1}{2}\times 4}} \right]\left[ {{5}^{\frac{1}{2}\times 4}} \right]={{5}^{2}}\times {{5}^{2}}={{5}^{4}}\]
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