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Question
Which one of the following is not equal to \[\left( \sqrt[3]{8} \right)^{- 1/2} ?\]
Options
\[\sqrt[3]{2}^{- 1/2}\]
\[8^{- 1/6}\]
\[\frac{1}{(\sqrt[3]{8} )^{1/2}}\]
\[\frac{1}{\sqrt{2}}\]
Solution
We have to find the value of `(3sqrt8)^(-1/2)`
So,
`(3sqrt8)^(-1/2) = (3sqrt(2xx 2xx 2))^(-1/2)`
`=(3sqrt(2^3))^(1/2)`
`2^(3 xx 1/3 xx -1/2)`
`2^(3 xx 1/3 xx -1/2)`
`(3sqrt8)^(-1/2) = 2^(-1/2)`
`= 1/(2^(1/2))`
`= 1/sqrt2`
Also, `(sqrt8)^(-1/2) = 2 ^(-1/6)`
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