<PAGE>   1
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ HOWARD H. BAKER, JR.
                                             -----------------------------
                                                 Howard H. Baker, Jr.
<PAGE>   2
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ W.L. LYONS BROWN, JR.
                                             -----------------------------
                                                 W.L. Lyons Brown, Jr.
<PAGE>   3
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ ERNEST H. COCKRELL
                                             -----------------------------
                                                 Ernest H. Cockrell
<PAGE>   4
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ ALFONSO FANJUL
                                             -----------------------------
                                                 Alfonso Fanjul
<PAGE>   5
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ C. FREDERICK FETTEROLF
                                             -----------------------------
                                                 C. Frederick Fetterolf
<PAGE>   6
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ FORREST R. HASELTON
                                             -----------------------------
                                                 Forrest R. Haselton
<PAGE>   7
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ BERDON LAWRENCE
                                             -----------------------------
                                                 Berdon Lawrence
<PAGE>   8
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ L. DAVID MYATT
                                             -----------------------------
                                                 L. David Myatt
<PAGE>   9
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ JAMES J. POSTL
                                             -----------------------------
                                                 James J. Postl
<PAGE>   10
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ GERALD B. SMITH
                                             -----------------------------
                                                 Gerald B. Smith
<PAGE>   11
                         PENNZOIL-QUAKER STATE COMPANY

                               POWER OF ATTORNEY


     WHEREAS, PENNZOIL-QUAKER STATE 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 capacity as a director or officer, 
or both, as the case may be, of the Company, does hereby appoint DAVID P. 
ALDERSON II, JAMES L. PATE and JAMES J. POSTL and each of them severally, his 
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 name, place and stead, in his 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 
10th day of March, 1999.


                                             /s/ LORNE R. WAXLAX
                                             -----------------------------
                                                 Lorne R. Waxlax