Question

Why does an.aqueous solution of a.base conduct electricity

Answer 1

This is because in aqueous solution ions may be free state and flow easily on applying current.

Answer 2

when we dissolve base in aqueous solution , it form alkaline ,
actually,water act as a separating the ions present in the alkaline
and you know that ions was carried charge..
so as the base dissociate in cation and anion
which have the tendency to conduct electricity
for example let's take an example of NaOH
when we dissolve in water its format for solution of be that is its form an alkali and dissociate into ions i.e Na+ & OH-
which conduct electricity
that's why an aqua solution of a base conduct electricity....
the same case happened with acid also...

may it help you !!! ^_^