<PAGE>   1
                                                                      Exhibit 24


                                POWER OF ATTORNEY

                  KNOW ALL MEN BY THESE PRESENTS, that the undersigned
constitutes and appoints J. Steven Whisler, Ramiro G. Peru and Robert C. Swan
and each of them his true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities:

Annual Report For the Year Ended December 31, 2000 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 2000 of Phelps Dodge Corporation on Form 10-K ("2000 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 2000 Form 10-K;

                  (2) to file such 2000 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 2000 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

                  IN WITNESS WHEREOF, the undersigned has executed this Power of
Attorney this 17th day of November, 2000.

                                              /s/ Robert N. Burt
                                              ----------------------------------
                                              Robert N. Burt
<PAGE>   2
                                POWER OF ATTORNEY

                  KNOW ALL MEN BY THESE PRESENTS, that the undersigned
constitutes and appoints J. Steven Whisler, Ramiro G. Peru and Robert C. Swan
and each of them his true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities:

Annual Report For the Year Ended December 31, 2000 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 2000 of Phelps Dodge Corporation on Form 10-K ("2000 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 2000 Form 10-K;

                  (2) to file such 2000 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 2000 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

                  IN WITNESS WHEREOF, the undersigned has executed this Power of
Attorney this 17th day of November, 2000.

                                          /s/ Archie W. Dunham
                                          -----------------------------------
                                          Archie W. Dunham
<PAGE>   3
                                POWER OF ATTORNEY

                  KNOW ALL MEN BY THESE PRESENTS, that the undersigned
constitutes and appoints J. Steven Whisler, Ramiro G. Peru and Robert C. Swan
and each of them his true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities:

Annual Report For the Year Ended December 31, 2000 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 2000 of Phelps Dodge Corporation on Form 10-K ("2000 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 2000 Form 10-K;

                  (2) to file such 2000 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 2000 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

                  IN WITNESS WHEREOF, the undersigned has executed this Power of
Attorney this 17th day of November, 2000.

                                           /s/ William A. Franke
                                           -------------------------------------
                                           William A. Franke
<PAGE>   4
                                POWER OF ATTORNEY

                  KNOW ALL MEN BY THESE PRESENTS, that the undersigned
constitutes and appoints J. Steven Whisler, Ramiro G. Peru and Robert C. Swan
and each of them his true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities:

Annual Report For the Year Ended December 31, 2000 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 2000 of Phelps Dodge Corporation on Form 10-K ("2000 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 2000 Form 10-K;

                  (2) to file such 2000 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 2000 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

                  IN WITNESS WHEREOF, the undersigned has executed this Power of
Attorney this 17th day of November, 2000.

                                                /s/ Paul Hazen
                                                --------------------------
                                                Paul Hazen
<PAGE>   5
                                POWER OF ATTORNEY

                  KNOW ALL MEN BY THESE PRESENTS, that the undersigned
constitutes and appoints J. Steven Whisler, Ramiro G. Peru and Robert C. Swan
and each of them his true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities:

Annual Report For the Year Ended December 31, 2000 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 2000 of Phelps Dodge Corporation on Form 10-K ("2000 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 2000 Form 10-K;

                  (2) to file such 2000 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 2000 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

                  IN WITNESS WHEREOF, the undersigned has executed this Power of
Attorney this 17th day of November, 2000.

                                             /s/ Manuel J. Iraola
                                            ------------------------------------
                                            Manuel J. Iraola
<PAGE>   6
                                POWER OF ATTORNEY

                  KNOW ALL MEN BY THESE PRESENTS, that the undersigned
constitutes and appoints J. Steven Whisler, Ramiro G. Peru and Robert C. Swan
and each of them her true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for her and in her name, place and stead, in
any and all capacities:

Annual Report For the Year Ended December 31, 2000 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 2000 of Phelps Dodge Corporation on Form 10-K ("2000 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 2000 Form 10-K;

                  (2) to file such 2000 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 2000 Form 10-K;

as fully to all intents and purposes as she might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or her substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

                  IN WITNESS WHEREOF, the undersigned has executed this Power of
Attorney this 17th day of November, 2000.

                                        /s/ Marie L. Knowles
                                        ---------------------------------------
                                        Marie L. Knowles
<PAGE>   7
                                POWER OF ATTORNEY

                  KNOW ALL MEN BY THESE PRESENTS, that the undersigned
constitutes and appoints J. Steven Whisler, Ramiro G. Peru and Robert C. Swan
and each of them his true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities:

Annual Report For the Year Ended December 31, 2000 of Phelps Dodge Corporation
on Form 10-K


                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 2000 of Phelps Dodge Corporation on Form 10-K ("2000 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 2000 Form 10-K;

                  (2) to file such 2000 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 2000 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

                  IN WITNESS WHEREOF, the undersigned has executed this Power of
Attorney this 17th day of November, 2000.

                                         /s/ Robert D. Krebs
                                        ------------------------------------
                                        Robert D. Krebs
<PAGE>   8
                                POWER OF ATTORNEY

                  KNOW ALL MEN BY THESE PRESENTS, that the undersigned
constitutes and appoints J. Steven Whisler, Ramiro G. Peru and Robert C. Swan
and each of them his true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities:

Annual Report For the Year Ended December 31, 2000 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 2000 of Phelps Dodge Corporation on Form 10-K ("2000 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 2000 Form 10-K;

                  (2) to file such 2000 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 2000 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

                  IN WITNESS WHEREOF, the undersigned has executed this Power of
Attorney this 17th day of November, 2000.

                                         /s/ Southwood J. Morcott
                                         -----------------------------------
                                         Southwood J. Morcott
<PAGE>   9
                                POWER OF ATTORNEY

                  KNOW ALL MEN BY THESE PRESENTS, that the undersigned
constitutes and appoints J. Steven Whisler, Ramiro G. Peru and Robert C. Swan
and each of them his true and lawful attorney-in-fact and agent, with full power
of substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities:

Annual Report For the Year Ended December 31, 2000 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 2000 of Phelps Dodge Corporation on Form 10-K ("2000 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 2000 Form 10-K;

                  (2) to file such 2000 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 2000 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

                  IN WITNESS WHEREOF, the undersigned has executed this Power of
Attorney this 22nd day of November, 2000.

                                           /s/ Gordon R. Parker
                                           -----------------------------------
                                           Gordon R. Parker
<PAGE>   10
                                POWER OF ATTORNEY

                  KNOW ALL MEN BY THESE PRESENTS, that the undersigned
constitutes and appoints Ramiro G. Peru and Robert C. Swan and each of them his
true and lawful attorney-in-fact and agent, with full power of substitution and
resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 2000 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 2000 of Phelps Dodge Corporation on Form 10-K ("2000 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 2000 Form 10-K;

                  (2) to file such 2000 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 2000 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

                  IN WITNESS WHEREOF, the undersigned has executed this Power of
Attorney this 17th day of November, 2000.

                                         /s/ J. Steven Whisler
                                         ------------------------------------
                                         J. Steven Whisler