Question

`((a)/(b))^(x+y+z)div[(sqrt(a/b))^(-x)xx(sqrta/b)^(-y)xx(sqrt(a/b))^(-z)]=`________.
A. `[a^3//b^3]^(x+y+z) `
B. `[a^2//b^2]^(x+y+z)`
C. `[a//b]^(x+y+z)//2`
D. `[a//b]^3(x+y+z)//2`

Answer 1

Correct Answer - D
`((a)/(b))^(x+y+z)div[(sqrt(a/b))^(-x)xx(sqrta/b)^(-y)xx(sqrt(a/b))^(-z)]`
`=((a)/(b))^(x+y+z)div[(a/b)^(-(x)/(2))xx(a/b)^(-(y)/(2))xx(a/b)^(-(z)/(2))]`
`=((a)/(b))^(x+y+z)div[(a/b)^(-((x+y+z)/(2)))]`
`=(a/b)^((3(x+y+z))/(2))`
Hence the correct option is (d).