At first he earned his living as a merchant, but he devoted himself to the field of education when he saw the level of Torah study wane in Baghdad. Hakham Abdallah became head of the yeshiva Midrash Abu Menashe (established in 1840 by Heskel Menashe Zebaida); the yeshiva was later expanded and renamed Midrash Beit Zilkha and remained in operation until 1951.
As rosh yeshiva, Hakham Somekh was teacher of several Sephardi sages including his brother-in-law, Rabbi Yosef Chaim ("the Ben Ish Chai"), and Rabbi Yaakov Chaim Sofer ("the Kaf HaChaim"). He issued a great number of rulings, particularly in matters of shechita (Jewish slaughter of animals) and treifot—these rulings have been published in the work Zivhei Tzedek (Baghdad 1914, 2 vols), which became the handbook for Baghdadi Jews thorughout India and the Far East. He also authored Responsa on all of the Shulchan Aruch. Hakham Abdallah died on Friday night 13 September 1889 during a cholera epidemic, and he was buried in the courtyard of the tomb of Yehoshua Kohen Gadol.