Question

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

Options

• \[\left\{ \left( \frac{5}{6} \right)^\frac{1}{5} \right\}^{- \frac{3}{6}}\]

• \[\frac{1}{\left\{ \left( \frac{5}{6} \right)^{1/5} \right\}^{1/6}}\]

• \[\left( \frac{6}{5} \right)^{1/30}\]

• \[\left( \frac{5}{6} \right)^{- 1/30}\]

Answer 1

We have to find the value of `{(5/6)^(1/5)}^((-1) / 6)`

So,

`{(5/6)^(1/5)}^((-1) / 6) = 5^(1/5 xx (-1)/6) / 6^(1/5 xx (-1)/6)`

`=5^(-1/30)/(6^((-1)/30))`

`=(1/(5^(-1/30))) / (1/(6^(1/30))`

 `{(5/6)^(1/5)}^((-1) / 6)` = `1/(5^(1/30)) xx (6^(1/30))/1`

                = `(6^(1/30))/5^(1/30)`

                = `(6/5)^(1/30)`