POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Jean Liu, Todd Simpson,
and Elizabeth Bekiroglu, each of them, his or her true and lawful attorney-in-
fact to:

(1)     execute for and on behalf of the undersigned, in the undersigned's
        capacity as an officer, director, and/or person who holds more than 10%
        of the stock of Seagen Inc. (the "Company"), Forms 3, Forms 4 and Forms
        5 in accordance with Section 16(a) of the Securities Exchange Act of
        1934, as amended (the "Exchange Act"), and the rules thereunder;

(2)     do and perform any and all acts for and on behalf of the undersigned
        which may be necessary or desirable to complete and execute any such
        Forms 3, Forms 4 or Forms 5 and timely file any such forms with the
        United States Securities and Exchange Commission and any other
        authority; and

(3)     take any other action of any type whatsoever in connection with the
        foregoing which, in the opinion of such attorney-in-fact, may be of
        benefit to, in the best interest of, or legally required by, the
        undersigned, it being understood that the documents executed by such
        attorney-in-fact on behalf of the undersigned, pursuant to this Power
        of Attorney shall be in such form and shall contain such terms and
        conditions as such attorney-in-fact may approve in his or her
        discretion.

        The undersigned hereby grants to each such attorney-in-fact full power
and authority to do and perform any and every act and thing whatsoever
requisite, necessary or proper to be done in the exercise of any of the rights
and powers herein granted, as fully to all intents and purposes as the
undersigned might or could do if personally present, with full power of
substitution or revocation, hereby ratifying and confirming all that such
attorney-in-fact, or his or her substitute or substitutes, shall lawfully do or
cause to be done pursuant to this power of attorney. The undersigned
acknowledges that the foregoing attorneys-in-fact, in serving in such capacity
at the request of the undersigned, are not assuming, nor is the Company
assuming, any of the undersigned's responsibilities to comply with Section 16
of the Exchange Act.

        This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, Forms 4, and Forms 5 with
respect to the undersigned's holdings of and transactions in securities issued
by the Company, unless earlier revoked by the undersigned in a signed writing
delivered to the attorneys-in-fact.

        The undersigned has caused this Power of Attorney to be executed as of
this 14th day of May 2021.

                                   /s/ Nancy Simonian, MD
                                   -------------------------------
                                   Nancy Simonian, MD