For a weak acid you can determine the value of the base dissociation constant ##K_b## of its 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))##