For a weak acid, you can determine the value of the base dissociation constant, #K_b#, of its conjugate base by using the water dissociation constant, #K_W#.
Mathematically, the relationship that exists between #K_a#, #K_b#, and #K_W# can be written like this
#K_W = K_a * K_b = 10^(-14)#
In the case of the hypobromite ion, #BrO^(-)#, the base dissociation constant will be
#K_b = 10^(-14)/K_a#
#K_b = 10^(-14)/(2.8 * 10^(-9)) = color(green)(3.6 * 10^(-6))#
The same is tru for dimethylamine, #(CH_3)_2NH#, and its conjugate acid, the dimethylammonium ion, #(CH_3)_2NH_2^(+)#.
#K_a = 10^(-14)/K_b#
#K_a = 10^(-14)/(5.4 * 10^(-4)) = color(green)(1.9 * 10^(-11))#
