
<PAGE>
                                                                      EXHIBIT 24
 
                               POWER OF ATTORNEY
 
    KNOW ALL MEN BY THESE PRESENTS, that REGIS CORPORATION, a Minnesota
corporation (the "Company"), and each of the undersigned directors of the
Company, hereby constitutes and appoints Paul D. Finkelstein and Frank E.
Evangelist and each of them (with full power to each of them to act alone)
its/his/her true and lawful attorney-in-fact and agent, for it/him/her and on
it/his/ her behalf and in its/his/her name, place and stead, in any and all
capacities to sign, execute, affix its/ his/her seal thereto and file a
Registration Statement on Form S-4 or any other applicable form under the
Securities Act of 1933, as amended, and amendments thereto, including
pre-effective and post-effective amendments, with all exhibits and any and all
documents required to be filed with respect thereto with any regulatory
authority, relating to the proposed registration of up to 5,000,000 shares of
the Company's Common Stock, par value $.05, reserved for issuance in connection
with the transactions contemplated by the Agreement and Plan of Merger by and
between the Company, RGIS Merger Corporation and Supercuts, Inc. dated as of
July 14, 1996.
 
    There is hereby granted to said attorneys, and each of them, full power and
authority to do and perform each and every act and thing requisite and necessary
to be done in respect of the foregoing as fully as it/he/she or
itself/himself/herself might or could do if personally present, hereby ratifying
and confirming all that said attorneys-in-fact and agents, or any of them, may
lawfully do or cause to be done by virtue hereof.
 
    This Power of Attorney may be executed in any number of counterparts, each
of which shall be an original, but all of which taken together shall constitute
one and the same instrument and any of the undersigned directors may execute
this Power of Attorney by signing any such counterpart.
 
    REGIS CORPORATION has caused this Power of Attorney to be executed in its
name by its Chief Executive Officer on the 6th day of August 1996.
 
                                          REGIS CORPORATION
                                          By       /s/ PAUL D. FINKELSTEIN
 
                                             -----------------------------------
                                                    Paul D. Finkelstein,
                                                   CHIEF EXECUTIVE OFFICER
<PAGE>
    The undersigned, directors of REGIS CORPORATION, have hereunto set their
hands as of the 6th day of August 1996.
 
<TABLE>
<S>                                           <C>
              /s/ MYRON KUNIN                           /s/ PAUL D. FINKELSTEIN
- -------------------------------------------   -------------------------------------------
                Myron Kunin                               Paul D. Finkelstein
 
          /s/ FRANK E. EVANGELIST                        /s/ CHRISTOPHER A. FOX
- -------------------------------------------   -------------------------------------------
            Frank E. Evangelist                            Christopher A. Fox
 
            /s/ ROLF F. BJELLAND                           /s/ VAN ZANDT HAWN
- -------------------------------------------   -------------------------------------------
              Rolf F. Bjelland                               Van Zandt Hawn
 
               /S/ SUSAN HOYT
- -------------------------------------------
                 Susan Hoyt
</TABLE>
 
                                       2
