The term "power bounded" refers to the capability of a system or an individual to remain within a specific limit of power or control. One possible synonym for "power bounded" is "constrained," which signifies the imposition of limitations or restrictions. Another synonym is "circumscribed," which suggests a border or boundary within which one's power or authority is defined. "Restricted" is another synonym that depicts a state of confinement or limitation. Other alternatives include "tethered," "regulated," "governed," and "moderated," each of which emphasizes the concept of containing or controlling power to prevent excess or abuse. Ultimately, the choice of a suitable synonym depends on the context and intended meaning of the phrase.