<PAGE>   1


                                                                    Exhibit 24.0


                                POWER OF ATTORNEY

                             COOPER INDUSTRIES, INC.



           KNOW ALL MEN BY THESE PRESENTS, that the undersigned director or
officer of Cooper Industries, Inc. ("Cooper"), an Ohio corporation, does hereby
make, constitute and appoint Diane K. Schumacher and Terrance V. Helz, and each
of them acting individually, his true and lawful attorney with power to act
without the other and with full power of substitution, to execute, deliver and
file, for and on behalf of the undersigned, and in his name and in his capacity
or capacities as aforesaid, the Cooper Annual Report on Form 10-K with the
Securities and Exchange Commission under the Securities Exchange Act of 1934, as
amended, and any other documents in support thereof or supplemental thereto,
with respect to the fiscal year ended December 31, 1999, and any and all
amendments thereto. The undersigned hereby grants to said attorneys and each of
them full power and authority to do and perform each and every act and thing
whatsoever as said attorney or attorneys may deem necessary or advisable to
carry out fully the intent of the foregoing as the undersigned might or could do
personally or in the capacity or capacities as aforesaid, hereby ratifying and
confirming all acts and things which said attorney or attorneys may do or cause
to be done by virtue of these presents.

           IN WITNESS WHEREOF, the undersigned has hereunto set his hand this
8th day of February 2000.



                                             /s/ Linda A. Hill
                                             ----------------------------------
                                             Linda A. Hill


<PAGE>   2


                                POWER OF ATTORNEY

                             COOPER INDUSTRIES, INC.



           KNOW ALL MEN BY THESE PRESENTS, that the undersigned director or
officer of Cooper Industries, Inc. ("Cooper"), an Ohio corporation, does hereby
make, constitute and appoint Diane K. Schumacher and Terrance V. Helz, and each
of them acting individually, his true and lawful attorney with power to act
without the other and with full power of substitution, to execute, deliver and
file, for and on behalf of the undersigned, and in his name and in his capacity
or capacities as aforesaid, the Cooper Annual Report on Form 10-K with the
Securities and Exchange Commission under the Securities Exchange Act of 1934, as
amended, and any other documents in support thereof or supplemental thereto,
with respect to the fiscal year ended December 31, 1999, and any and all
amendments thereto. The undersigned hereby grants to said attorneys and each of
them full power and authority to do and perform each and every act and thing
whatsoever as said attorney or attorneys may deem necessary or advisable to
carry out fully the intent of the foregoing as the undersigned might or could do
personally or in the capacity or capacities as aforesaid, hereby ratifying and
confirming all acts and things which said attorney or attorneys may do or cause
to be done by virtue of these presents.

           IN WITNESS WHEREOF, the undersigned has hereunto set his hand this
8th day of February 2000.



                                             /s/ John D. Ong
                                             ----------------------------------
                                             John D. Ong


<PAGE>   3


                                POWER OF ATTORNEY

                             COOPER INDUSTRIES, INC.



           KNOW ALL MEN BY THESE PRESENTS, that the undersigned director or
officer of Cooper Industries, Inc. ("Cooper"), an Ohio corporation, does hereby
make, constitute and appoint Diane K. Schumacher and Terrance V. Helz, and each
of them acting individually, his true and lawful attorney with power to act
without the other and with full power of substitution, to execute, deliver and
file, for and on behalf of the undersigned, and in his name and in his capacity
or capacities as aforesaid, the Cooper Annual Report on Form 10-K with the
Securities and Exchange Commission under the Securities Exchange Act of 1934, as
amended, and any other documents in support thereof or supplemental thereto,
with respect to the fiscal year ended December 31, 1999, and any and all
amendments thereto. The undersigned hereby grants to said attorneys and each of
them full power and authority to do and perform each and every act and thing
whatsoever as said attorney or attorneys may deem necessary or advisable to
carry out fully the intent of the foregoing as the undersigned might or could do
personally or in the capacity or capacities as aforesaid, hereby ratifying and
confirming all acts and things which said attorney or attorneys may do or cause
to be done by virtue of these presents.

           IN WITNESS WHEREOF, the undersigned has hereunto set his hand this
8th day of February 2000.



                                                  /s/ Sir Ralph H. Robins
                                                  ------------------------------
                                                  Sir Ralph H. Robins


<PAGE>   4


                                POWER OF ATTORNEY

                             COOPER INDUSTRIES, INC.



           KNOW ALL MEN BY THESE PRESENTS, that the undersigned director or
officer of Cooper Industries, Inc. ("Cooper"), an Ohio corporation, does hereby
make, constitute and appoint Diane K. Schumacher and Terrance V. Helz, and each
of them acting individually, his true and lawful attorney with power to act
without the other and with full power of substitution, to execute, deliver and
file, for and on behalf of the undersigned, and in his name and in his capacity
or capacities as aforesaid, the Cooper Annual Report on Form 10-K with the
Securities and Exchange Commission under the Securities Exchange Act of 1934, as
amended, and any other documents in support thereof or supplemental thereto,
with respect to the fiscal year ended December 31, 1999, and any and all
amendments thereto. The undersigned hereby grants to said attorneys and each of
them full power and authority to do and perform each and every act and thing
whatsoever as said attorney or attorneys may deem necessary or advisable to
carry out fully the intent of the foregoing as the undersigned might or could do
personally or in the capacity or capacities as aforesaid, hereby ratifying and
confirming all acts and things which said attorney or attorneys may do or cause
to be done by virtue of these presents.

           IN WITNESS WHEREOF, the undersigned has hereunto set his hand this
8th day of February 2000.



                                                  /s/ H. Lee Scott
                                                  ------------------------------
                                                  H. Lee Scott



<PAGE>   5


                                POWER OF ATTORNEY

                             COOPER INDUSTRIES, INC.



           KNOW ALL MEN BY THESE PRESENTS, that the undersigned director or
officer of Cooper Industries, Inc. ("Cooper"), an Ohio corporation, does hereby
make, constitute and appoint Diane K. Schumacher and Terrance V. Helz, and each
of them acting individually, his true and lawful attorney with power to act
without the other and with full power of substitution, to execute, deliver and
file, for and on behalf of the undersigned, and in his name and in his capacity
or capacities as aforesaid, the Cooper Annual Report on Form 10-K with the
Securities and Exchange Commission under the Securities Exchange Act of 1934, as
amended, and any other documents in support thereof or supplemental thereto,
with respect to the fiscal year ended December 31, 1999, and any and all
amendments thereto. The undersigned hereby grants to said attorneys and each of
them full power and authority to do and perform each and every act and thing
whatsoever as said attorney or attorneys may deem necessary or advisable to
carry out fully the intent of the foregoing as the undersigned might or could do
personally or in the capacity or capacities as aforesaid, hereby ratifying and
confirming all acts and things which said attorney or attorneys may do or cause
to be done by virtue of these presents.

           IN WITNESS WHEREOF, the undersigned has hereunto set his hand this
8th day of February 2000.



                                                  /s/ Dan F. Smith
                                                  -----------------------------
                                                  Dan F. Smith


<PAGE>   6


                                POWER OF ATTORNEY

                             COOPER INDUSTRIES, INC.



           KNOW ALL MEN BY THESE PRESENTS, that the undersigned director or
officer of Cooper Industries, Inc. ("Cooper"), an Ohio corporation, does hereby
make, constitute and appoint Diane K. Schumacher and Terrance V. Helz, and each
of them acting individually, his true and lawful attorney with power to act
without the other and with full power of substitution, to execute, deliver and
file, for and on behalf of the undersigned, and in his name and in his capacity
or capacities as aforesaid, the Cooper Annual Report on Form 10-K with the
Securities and Exchange Commission under the Securities Exchange Act of 1934, as
amended, and any other documents in support thereof or supplemental thereto,
with respect to the fiscal year ended December 31, 1999, and any and all
amendments thereto. The undersigned hereby grants to said attorneys and each of
them full power and authority to do and perform each and every act and thing
whatsoever as said attorney or attorneys may deem necessary or advisable to
carry out fully the intent of the foregoing as the undersigned might or could do
personally or in the capacity or capacities as aforesaid, hereby ratifying and
confirming all acts and things which said attorney or attorneys may do or cause
to be done by virtue of these presents.

           IN WITNESS WHEREOF, the undersigned has hereunto set his hand this
8th day of February 2000.



                                             /s/ James R. Wilson
                                             -----------------------------------
                                             James R. Wilson