In addition to the powers conferred upon the board of regents of the University of Washington by RCW
28B.20.395, the board of regents is authorized and shall have the power to enter into an agreement or agreements with the city of Seattle and the county of King, Washington, to pay to the city and the county such sums as shall be mutually agreed upon for governmental services rendered to the university tract, which sums shall not exceed the amounts that would be received pursuant to limitations imposed by RCW
84.52.043 by the city of Seattle and county of King respectively from real and personal property taxes paid on the university tract or any leaseholds thereon if such taxes could lawfully be levied.