<PAGE>   1


                                                                     EXHIBIT 24


                               POWERS OF ATTORNEY



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                               POWER OF ATTORNEY


         I, the undersigned director of United States Exploration, Inc., do
hereby constitute and appoint Bruce D. Benson and F. Michael Murphy, or either
of them, to be my true and lawful attorneys-in-fact and agents, with full power
of substitution and resubstitution, and in my name, place and stead, in any and
all capacities, to sign to the Company's Annual Report on Form 10-KSB for the
year ended December 31, 1998 and any and all amendments thereto, and to file
the same, with all exhibits thereto, and other documents in connection
therewith, with the Securities and Exchange Commission, granting unto said
attorneys-in-fact and agents full power and authority to do and perform each
and every act and thing requisite and necessary to be done in connection
therewith and about the premises, as fully to all intents and purposes as I
might or could do in person, hereby ratifying and confirming all that said
attorneys-in-fact and agents, or any of them, or their or his substitute or
substitutes, may lawfully do or cause to be done by virtue thereof.

         Dated this 15th day of April, 1999.



                                       /s/ Richard L. Robinson
                                       -----------------------------------------
                                       Richard L. Robinson, Director



<PAGE>   3


                               POWER OF ATTORNEY


         I, the undersigned director of United States Exploration, Inc., do
hereby constitute and appoint Bruce D. Benson and F. Michael Murphy, or either
of them, to be my true and lawful attorneys-in-fact and agents, with full power
of substitution and resubstitution, and in my name, place and stead, in any and
all capacities, to sign to the Company's Annual Report on Form 10-KSB for the
year ended December 31, 1998 and any and all amendments thereto, and to file
the same, with all exhibits thereto, and other documents in connection
therewith, with the Securities and Exchange Commission, granting unto said
attorneys-in-fact and agents full power and authority to do and perform each
and every act and thing requisite and necessary to be done in connection
therewith and about the premises, as fully to all intents and purposes as I
might or could do in person, hereby ratifying and confirming all that said
attorneys-in-fact and agents, or any of them, or their or his substitute or
substitutes, may lawfully do or cause to be done by virtue thereof.

         Dated this 15th day of April, 1999.



                                       /s/ Thomas W. Gamel
                                       -----------------------------------------
                                       Thomas W. Gamel, Director



<PAGE>   4


                               POWER OF ATTORNEY


         I, the undersigned director of United States Exploration, Inc., do
hereby constitute and appoint Bruce D. Benson and F. Michael Murphy, or either
of them, to be my true and lawful attorneys-in-fact and agents, with full power
of substitution and resubstitution, and in my name, place and stead, in any and
all capacities, to sign to the Company's Annual Report on Form 10-KSB for the
year ended December 31, 1998 and any and all amendments thereto, and to file
the same, with all exhibits thereto, and other documents in connection
therewith, with the Securities and Exchange Commission, granting unto said
attorneys-in-fact and agents full power and authority to do and perform each
and every act and thing requisite and necessary to be done in connection
therewith and about the premises, as fully to all intents and purposes as I
might or could do in person, hereby ratifying and confirming all that said
attorneys-in-fact and agents, or any of them, or their or his substitute or
substitutes, may lawfully do or cause to be done by virtue thereof.

         Dated this 15th day of April, 1999.



                                       /s/ Robert J. Malone
                                       -----------------------------------------
                                       Robert J. Malone, Director