A) \[m=1\]
B) \[m=\frac{1}{3}\]
C) \[m=-\frac{1}{3}\]
D) \[m=-7\]
Correct Answer: C
Solution :
[c] \[{{\left[ {{\left\{ {{\left( \frac{1}{{{7}^{2}}} \right)}^{-2}} \right\}}^{\frac{-1}{3}}} \right]}^{\frac{1}{4}}}={{7}^{m}}\] \[\Rightarrow \] \[{{\left[ {{\{{{({{7}^{-2}})}^{-2}}\}}^{-1/3}} \right]}^{\frac{1}{4}}}={{7}^{m}}\] \[\Rightarrow \] \[{{\left[ {{({{7}^{4}})}^{-1/3}} \right]}^{\frac{1}{4}}}={{7}^{m}}\] \[\Rightarrow \] \[{{({{7}^{-4/3}})}^{1/4}}={{7}^{m}}\] \[\Rightarrow \] \[{{7}^{-1/3}}={{7}^{m}}\] \[\therefore \] \[m=-1/3\]
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