Decreasing rate of Earth's rotation: where does the power go? I understand from Wikipedia that, "The length of the day, which has increased over the long term of Earth's history due to tidal effects, ...".  If the angular velocity of the earth is decreasing then the stored rotational energy is decreasing.  Where does the power/energy go?
You're correct in assuming the net angular momentum of the system in question here will remain constant. The Moon's orbit around Earth is responsible for the slowing of Earth's rotation. This effect is extremely small. 

The decrease in Earth's angular momentum is transferred to the moon, which resultantly sees it's orbit accelerate. This acceleration also causes the moon to move further and further from the Earth. This trend will continue until they reach a common speed.