Question

Which of the following is (are) not equal to ${\left\{{\left(\frac{5}{6}\right)}^{\frac{1}{5}}\right\}}^{\frac{-1}{6}}$

Answer 1

${\left\{{\left(\frac{5}{6}\right)}^{\frac{1}{5}}\right\}}^{\frac{-1}{6}}\ne {\left(\frac{5}{6}\right)}^{\frac{1}{5}-\frac{1}{6}}$

Now, ${\left\{{\left(\frac{5}{6}\right)}^{\frac{1}{5}}\right\}}^{\frac{-1}{6}}$

$=\frac{1}{{\left\{{\left(\frac{5}{6}\right)}^{\frac{1}{5}}\right\}}^{\frac{1}{6}}}$

$=\frac{1}{{\left(\frac{5}{6}\right)}^{\frac{1}{5}\times \frac{1}{6}}}$

$=\frac{1}{{\left(\frac{5}{6}\right)}^{\frac{1}{30}}}$

$={\left(\frac{6}{5}\right)}^{\frac{1}{30}}$

$={\left(\frac{5}{6}\right)}^{\frac{-1}{30}}$

Clearly, option (a) is not equal.

Hence, (a) is correct answer.