Question

Answer question number 13

Answer 1

13.
9^(r+ 1/4) = 3^2(r + 1/4) = 3^(2r + 1/2)
Root(3*3^-r) = root(3^(1-r)) = 3^(1-r)/2
Denominator: 3root3^-r = 3* 3^(-r/2) = 3^(1 - r/2)

Now L.H.S reads as:
Under root r { [ 3^(2r+1/2) * 3^(1-r)/2]/ 3^(1- r/2) }
Under root r { [ 3^(2r + 1/2 + 1/2 - r/2 -1 +r/2)]}
Under root r { [ 3^2r]}
[3^2r]^1/r
3^2
L.H.S = 3^2
R.H.S = k
Hence, K = 3^2
Option B

[concepts: a^m*a^n = a^(m+n).. a^m/a^n = a^(m-n)... root(a) = a^(1/2).. (a^m)^n = a^(m*n)]
Hope it helps.