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प्रश्न
Which of the following is (are) not equal to \[\left\{ \left( \frac{5}{6} \right)^{1/5} \right\}^{- 1/6}\] ?
विकल्प
\[\left\{ \left( \frac{5}{6} \right)^\frac{1}{5} \right\}^{- \frac{3}{6}}\]
\[\frac{1}{\left\{ \left( \frac{5}{6} \right)^{1/5} \right\}^{1/6}}\]
\[\left( \frac{6}{5} \right)^{1/30}\]
\[\left( \frac{5}{6} \right)^{- 1/30}\]
उत्तर
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)`
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