Upon appeals the Board of Adjustment shall have the following powers:

(1) To hear and decide appeals where it is alleged by the appellant that there is error in any order, requirement, decision or refusal made by an administrative official or agency based on or made in the enforcement of the zoning regulations;

(2) To hear and decide, in accordance with the provisions of any zoning regulations, requests for special exceptions or for interpretation of the map or for decisions upon other special questions upon which the Board is authorized by any zoning regulation to pass;

(3) Where by reason of exceptional narrowness, shallowness or shape of a specific piece of property at the time of the enactment of the regulations, 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 adopted under this subchapter would result in peculiar and exceptional practical difficulties to, or exceptional and undue hardship upon, the owner of such property, to authorize, upon an appeal relating to such property, a variance from such strict application so as to relieve such difficulties or hardship; provided such relief may be granted without substantial detriment to the public good and without substantially impairing the intent and purpose of the zoning plan and zoning regulations.

9 Del. C. 1953, § ?4917; 56 Del. Laws, c. 103, § ?16; 66 Del. Laws, c. 207, § ?1;