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Question
Find the value of k in each of the following:
`(root(3)(8))^((-1)/(2)` = 2k
Solution
`(root(3)(8))^((-1)/(2)` = 2k
⇒ `8^(1/3 xx (-1)/(2))` = 2k
⇒ `(2^3)^(1/3 xx (-1)/2)` = 2k
⇒ `(2^3)^(1/3 xx (-1)/2)` = 2k
⇒ `2^((-1)/(2)` = 2k
⇒ k = `-(1)/(2)`.
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