A nonresident owner, except as provided in sections 321.54 and 321.55, of a private passenger motor vehicle, not operated for hire, may operate or permit the operation of such vehicle within this state without registering such vehicle in, or paying any fees to, this state subject to the condition that such vehicle at all times when operated in this state is duly registered in, and displays upon it a valid registration plate or plates issued for such vehicle in the place of residence of such owner. A nonresident who leases a vehicle from a resident owner shall not be considered a nonresident owner of such vehicle for the purpose of exemption under this section. This section shall be operative to the extent that under the laws of the foreign country, state, territory, or federal district of such nonresident owner’s residence like exemptions and privileges are granted to vehicles registered under the laws, and owned by residents, of this state. A truck, truck tractor, trailer or semitrailer owned by a nonresident and operated on Iowa highways must have displayed upon it a valid registration plate or plates and a valid registration certificate, card, or other official evidence of its allowable weight in the state, district or county in which it is registered.