Mighty Emergence

The ability checks that creature's power only once: when that creature enters. The trigger checks a creature's initial power upon being put on the battlefield, so it will take into account counters that it enters with and static abilities that may give it a continuous power boost once it's on the battlefield (such as the one on Glorious Anthem). After the creature is already on the battlefield, boosting its power with a spell (such as Giant Growth), activated ability, or triggered ability won't allow this ability to trigger; it's too late by then. Once the ability triggers, it will resolve no matter what the creature's power may become while the ability is on the stack.