A) \[{{[{{({{5}^{-2}})}^{-2}}]}^{-2}}\]
B) \[{{[{{({{5}^{-2}})}^{2}}]}^{-2}}\]
C) \[{{[{{({{2}^{-5}})}^{-2}}]}^{-2}}\]
D) \[{{[{{({{2}^{-5}})}^{2}}]}^{-2}}\]
Correct Answer: C
Solution :
[a] \[{{[{{({{5}^{-2}})}^{-2}}]}^{2}}={{\left( \frac{1}{{{5}^{2}}} \right)}^{4}}={{\left( \frac{1}{25} \right)}^{4}}\] [b] \[{{[{{({{5}^{-2}})}^{-2}}]}^{2}}={{({{5}^{2}})}^{4}}={{(25)}^{4}}\] [c] \[{{[{{({{2}^{-5}})}^{-2}}]}^{-2}}={{\left( \frac{1}{{{2}^{5}}} \right)}^{4}}={{\left( \frac{1}{32} \right)}^{4}}\] [d] \[{{[{{({{2}^{5}})}^{2}}]}^{-2}}={{({{2}^{5}})}^{4}}={{\left( 32 \right)}^{4}}\] Smallest number = \[{{[{{({{2}^{-5}})}^{2}}]}^{-2}}\]
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