Advertisements
Advertisements
Question
Find the value of k in each of the following:
`(root(3)(8))^((-1)/(2)` = 2k
Advertisements
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)`.
APPEARS IN
RELATED QUESTIONS
Solve for x:
`3^(4x + 1) = (27)^(x + 1)`
Solve : 8 x 22x + 4 x 2x + 1 = 1 + 2x
Solve : `(sqrt(3))^( x - 3 ) = ( root(4)(3))^( x + 1 )`
Solve for x:
`(81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27`
Solve for x:
`2^(3x + 3) = 2^(3x + 1) + 48`
Evaluate the following:
`(8/27)^((-2)/3) - (1/3)^-2 - 7^0`
Find the value of k in each of the following:
`(sqrt(9))^-7 xx (sqrt(3))^-5` = 3k
If `root(x)("a") = root(y)("b") = root(z)("c")` and abc = 1, prove that x + y + z = 0
Find the value of 'a' and 'b' if:
92a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`
Prove the following:
`sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)` = 1
