Killing off a nest of ants may take a few years as they are tough to get at, as they are protected deep within their hollowed-out fortress.
The easiest way for homeowners to begin control is to spread ant powder all around the base of the tree and keep re-applying it every time it rains and disappears. The ants will need to walk through it as they leave the tree in search of food. The product will absorb through their feet and they will die at a later time, usually within the nest. As ants are carnivorous, they will cannibalize their own dead, and the poison will spread throughout the colony.
Please be aware that there is now poison around the tree, which can pose a threat to inquisitive pets or children.
We have found that ants typically live above the entrance hole. We assume this is the case so that any water that infiltrates the entrance hole can’t seep downward and flood the nest. If the entrance hole can be safely reached, activate a can of room defogger into the opening (the type that is meant to bug bomb a house for spiders and other bugs). If they are living above the hole, they will come flooding out by the thousands. Have a few aerosol cans of Raid or Ortho Ant Killer ready and spray the ants as they evacuate their ‘protected’ environment. Between those that are killed instantly and those that will feed off of the dead ant carcasses later, the problem should be able to be brought under control fairly quickly.