At or within two weeks of the time of fixing the date for such hearing the board shall appoint three qualified appraisers, at least one of whom shall be a resident of the county in which said district is situated, who shall qualify as provided in RCW 85.08.360. Thereupon said appraisers shall proceed immediately to carefully examine the district's system of improvements and the public and private property within the district, and fairly, justly and equitably determine and apportion the special benefits which will accrue from the maintenance of the district's system of improvements to each piece or parcel of privately and publicly owned land, together with the buildings and other permanent improvements thereon, and to the state, county, cities, towns and other municipal corporations for their roads and streets and other property within the district. The fact that any such property shall be exempt from general taxes shall not exempt the same from the provisions hereof.