Let’s do a couple first order approximations for this scene.
 
Based on various comparisons of pony sizes and houses, ponies are about 3 feet tall, and a single-story house is about 3-4 pony heights tall, or about 10 feet. Counting the branches and the roots, he Golden Oak Library is about three stories tall, making the tree about 30 feet, or roughly 9 meters tall. General Sherman, the largest living Sequoia Tree, is 274 feet tall, and weighs about 2.7 million pounds. The library has a roughly similar width, so as an estimate on its weight, let’s take 2.7 million divided by 9 (for the height), and then, since it’s hollowed out for use as a dwelling and has a higher proportion of branches, let’s quarter that weight again as an approximation, for a weight estimate of 75,000 pounds, or about 34,000 kilograms.
 
The tree rose about 4 times its own height, giving it an altitude of about 36 meters. Ignoring air resistance (which probably has a relatively minimal effect with this massive an object and the low duration of airtime) and assuming perfect energy transfer, the energy required to lift said object 36 meters into the air is U = 9.8 * 34000 * 36 = ~12 million Joules. Assuming that Twilight’s blast was omnidirectional, to get 12 million Joules applied in an upward direction, the total energy would have to be about 6 times that (12 million for each of the axes), for a total of 72 million Joules, or 72 MJ.
 
If we take the frames of the pink explosion as the time to impart said energy, then the magic took about 1/5 of a second. That would give Twilight’s magic in this scene Power of about 360 million Watts, or 360 MW. This is comparable to the peak power output of modern Aircraft Carriers.
 
No, this is not to be taken seriously.