The board of appeals has the power to:
(1) Hear and decide appeals where it is alleged by the appellant that there is error in any order, requirement, permit, decision, or refusal made by the municipal building commissioner or any other administrative official in the carrying out or enforcement of any provision of any ordinance enacted pursuant to this part and part 3 of this chapter;
(2) Hear and decide, in accordance with any such ordinance, requests for special exceptions or for interpretation of the map or for decisions upon other special questions upon which such board is authorized by any such ordinance to pass; and
(3) Where, by reason of exceptional narrowness, shallowness or shape of a specific piece of property at the time of the enactment of the zoning regulation, or by reason of exceptional topographic conditions or other extraordinary and exceptional situation or condition of such piece of property, the strict application of any regulation enacted under this part and part 3 of this chapter would result in peculiar and exceptional practical difficulties to or exception or undue hardship upon the owner of such property, authorize, upon an appeal relating to the property, a variance from such strict application so as to relieve such difficulties or hardship; provided, that such relief may be granted without substantial detriment to the public good and without substantially impairing the intent and purpose of the zone plan and zoning ordinance.