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Question
Find the value of k in each of the following:
`(sqrt(9))^-7 xx (sqrt(3))^-5` = 3k
Solution
`(sqrt(9))^-7 xx (sqrt(3))^-5` = 3k
⇒ `{(3^2)^(1/2)}^-7 {(3)^(1/2)}^-5` = 3k
⇒ `3^-7 xx 3^((-5)/2)` = 3k
⇒ `3^(-7 -5/2)` = 3k
⇒ `3^((-14 - 5)/(2)` = 3k
⇒ `3^((-19)/(2)` = 3k
⇒ k = `(-19)/(2)`.
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