| Simplify for the value of x. \[{{[{{[\sqrt[7]{({{x}^{-4/7}})}]}^{7/3}}]}^{21}}=\frac{1}{16}\] |
A) 1
B) 2
C) 3
D) 4
Correct Answer: B
Solution :
| \[{{\{{{[\sqrt[7]{{{x}^{-4/7}}}]}^{7/3}}\}}^{21}}=\frac{1}{16}\] |
| \[\Rightarrow \] \[{{\{{{[{{({{x}^{-4/7}})}^{1/7}}]}^{7/3}}\}}^{21}}=\frac{1}{16}\] |
| \[\Rightarrow \] \[{{[{{x}^{-4/7}}]}^{1/3\,\,\times \,}}^{21}=\frac{1}{16}\] |
| \[\Rightarrow \] \[{{x}^{-4}}={{16}^{-1}}={{2}^{-4}}\]\[\Rightarrow \]\[x=2\] |
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