<PAGE>   1
 
                              PENNZENERGY COMPANY
 
                               POWER OF ATTORNEY
 
     WHEREAS, PENNZENERGY COMPANY, a Delaware corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended (the "Act"), an Annual
Report on Form 10-K for the fiscal year ended December 31, 1998, as prescribed
by the Commission pursuant to the Act and the rules and regulations of the
Commission promulgated thereunder, with such amendments, supplements or
appendices thereto as may be necessary or appropriate, together with any and all
exhibits and other documents having relation to said Annual Report;
 
     NOW, THEREFORE, the undersigned in his or her capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint
STEPHEN D. CHESEBRO, BRUCE K. MISAMORE and JAMES L. PATE and each of them
severally, his or her true and lawful attorney or attorneys with power to act
with or without the others, and with full power of substitution and
resubstitution, to execute in his or her name, place and stead, in his or her
capacity as a director or officer, or both, as the case may be, of the Company,
said Annual Report and any and all amendments, supplements or appendices thereto
as said attorneys or any of them shall deem necessary or incidental in
connection therewith and to file the same or cause the same to be filed with the
Commission. Each of said attorneys shall have full power and authority to do and
perform in the name and on behalf of the undersigned in any and all capacities,
every act whatsoever necessary or desirable to be done to the premises, as fully
and to all intents and purposes as the undersigned might or could do in person,
the undersigned hereby ratifying and approving the acts of said attorneys and
each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument on this
17th day of February, 1999.
 
                                                      HENRY R. HAMMAN
 
                                          --------------------------------------
<PAGE>   2
 
                              PENNZENERGY COMPANY
 
                               POWER OF ATTORNEY
 
     WHEREAS, PENNZENERGY COMPANY, a Delaware corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended (the "Act"), an Annual
Report on Form 10-K for the fiscal year ended December 31, 1998, as prescribed
by the Commission pursuant to the Act and the rules and regulations of the
Commission promulgated thereunder, with such amendments, supplements or
appendices thereto as may be necessary or appropriate, together with any and all
exhibits and other documents having relation to said Annual Report;
 
     NOW, THEREFORE, the undersigned in his or her capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint
STEPHEN D. CHESEBRO, BRUCE K. MISAMORE and JAMES L. PATE and each of them
severally, his or her true and lawful attorney or attorneys with power to act
with or without the others, and with full power of substitution and
resubstitution, to execute in his or her name, place and stead, in his or her
capacity as a director or officer, or both, as the case may be, of the Company,
said Annual Report and any and all amendments, supplements or appendices thereto
as said attorneys or any of them shall deem necessary or incidental in
connection therewith and to file the same or cause the same to be filed with the
Commission. Each of said attorneys shall have full power and authority to do and
perform in the name and on behalf of the undersigned in any and all capacities,
every act whatsoever necessary or desirable to be done to the premises, as fully
and to all intents and purposes as the undersigned might or could do in person,
the undersigned hereby ratifying and approving the acts of said attorneys and
each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument on this
17th day of February, 1999.
 
                                                   ROBERT MOSBACHER, JR.
 
                                          --------------------------------------
<PAGE>   3
 
                              PENNZENERGY COMPANY
 
                               POWER OF ATTORNEY
 
     WHEREAS, PENNZENERGY COMPANY, a Delaware corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended (the "Act"), an Annual
Report on Form 10-K for the fiscal year ended December 31, 1998, as prescribed
by the Commission pursuant to the Act and the rules and regulations of the
Commission promulgated thereunder, with such amendments, supplements or
appendices thereto as may be necessary or appropriate, together with any and all
exhibits and other documents having relation to said Annual Report;
 
     NOW, THEREFORE, the undersigned in his or her capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint
STEPHEN D. CHESEBRO, BRUCE K. MISAMORE and JAMES L. PATE and each of them
severally, his or her true and lawful attorney or attorneys with power to act
with or without the others, and with full power of substitution and
resubstitution, to execute in his or her name, place and stead, in his or her
capacity as a director or officer, or both, as the case may be, of the Company,
said Annual Report and any and all amendments, supplements or appendices thereto
as said attorneys or any of them shall deem necessary or incidental in
connection therewith and to file the same or cause the same to be filed with the
Commission. Each of said attorneys shall have full power and authority to do and
perform in the name and on behalf of the undersigned in any and all capacities,
every act whatsoever necessary or desirable to be done to the premises, as fully
and to all intents and purposes as the undersigned might or could do in person,
the undersigned hereby ratifying and approving the acts of said attorneys and
each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument on this
17th day of February, 1999.
 
                                                      TERRY L. SAVAGE
 
                                          --------------------------------------
<PAGE>   4
 
                              PENNZENERGY COMPANY
 
                               POWER OF ATTORNEY
 
     WHEREAS, PENNZENERGY COMPANY, a Delaware corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended (the "Act"), an Annual
Report on Form 10-K for the fiscal year ended December 31, 1998, as prescribed
by the Commission pursuant to the Act and the rules and regulations of the
Commission promulgated thereunder, with such amendments, supplements or
appendices thereto as may be necessary or appropriate, together with any and all
exhibits and other documents having relation to said Annual Report;
 
     NOW, THEREFORE, the undersigned in his or her capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint
STEPHEN D. CHESEBRO, BRUCE K. MISAMORE and JAMES L. PATE and each of them
severally, his or her true and lawful attorney or attorneys with power to act
with or without the others, and with full power of substitution and
resubstitution, to execute in his or her name, place and stead, in his or her
capacity as a director or officer, or both, as the case may be, of the Company,
said Annual Report and any and all amendments, supplements or appendices thereto
as said attorneys or any of them shall deem necessary or incidental in
connection therewith and to file the same or cause the same to be filed with the
Commission. Each of said attorneys shall have full power and authority to do and
perform in the name and on behalf of the undersigned in any and all capacities,
every act whatsoever necessary or desirable to be done to the premises, as fully
and to all intents and purposes as the undersigned might or could do in person,
the undersigned hereby ratifying and approving the acts of said attorneys and
each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument on this
17th day of February, 1999.
 
                                                      BRENT SCOWCROFT
 
                                          --------------------------------------
<PAGE>   5
 
                              PENNZENERGY COMPANY
 
                               POWER OF ATTORNEY
 
     WHEREAS, PENNZENERGY COMPANY, a Delaware corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended (the "Act"), an Annual
Report on Form 10-K for the fiscal year ended December 31, 1998, as prescribed
by the Commission pursuant to the Act and the rules and regulations of the
Commission promulgated thereunder, with such amendments, supplements or
appendices thereto as may be necessary or appropriate, together with any and all
exhibits and other documents having relation to said Annual Report;
 
     NOW, THEREFORE, the undersigned in his or her capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint
STEPHEN D. CHESEBRO, BRUCE K. MISAMORE and JAMES L. PATE and each of them
severally, his or her true and lawful attorney or attorneys with power to act
with or without the others, and with full power of substitution and
resubstitution, to execute in his or her name, place and stead, in his or her
capacity as a director or officer, or both, as the case may be, of the Company,
said Annual Report and any and all amendments, supplements or appendices thereto
as said attorneys or any of them shall deem necessary or incidental in
connection therewith and to file the same or cause the same to be filed with the
Commission. Each of said attorneys shall have full power and authority to do and
perform in the name and on behalf of the undersigned in any and all capacities,
every act whatsoever necessary or desirable to be done to the premises, as fully
and to all intents and purposes as the undersigned might or could do in person,
the undersigned hereby ratifying and approving the acts of said attorneys and
each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument on this
17th day of February, 1999.
 
                                                       JAMES L. PATE
 
                                          --------------------------------------
<PAGE>   6
 
                              PENNZENERGY COMPANY
 
                               POWER OF ATTORNEY
 
     WHEREAS, PENNZENERGY COMPANY, a Delaware corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended (the "Act"), an Annual
Report on Form 10-K for the fiscal year ended December 31, 1998, as prescribed
by the Commission pursuant to the Act and the rules and regulations of the
Commission promulgated thereunder, with such amendments, supplements or
appendices thereto as may be necessary or appropriate, together with any and all
exhibits and other documents having relation to said Annual Report;
 
     NOW, THEREFORE, the undersigned in his or her capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint
STEPHEN D. CHESEBRO, BRUCE K. MISAMORE and JAMES L. PATE and each of them
severally, his or her true and lawful attorney or attorneys with power to act
with or without the others, and with full power of substitution and
resubstitution, to execute in his or her name, place and stead, in his or her
capacity as a director or officer, or both, as the case may be, of the Company,
said Annual Report and any and all amendments, supplements or appendices thereto
as said attorneys or any of them shall deem necessary or incidental in
connection therewith and to file the same or cause the same to be filed with the
Commission. Each of said attorneys shall have full power and authority to do and
perform in the name and on behalf of the undersigned in any and all capacities,
every act whatsoever necessary or desirable to be done to the premises, as fully
and to all intents and purposes as the undersigned might or could do in person,
the undersigned hereby ratifying and approving the acts of said attorneys and
each of them.
 
     IN WITNESS WHEREOF, the undersigned has executed this instrument on this
17th day of February, 1999.
 
                                                     ROBERT B. WEAVER
 
                                          --------------------------------------