When i driving about 25 mph and hit bumps the whole car shakes violently and my tire jump out 8 inches back and fourth and it doest stop until the car slows down

Could be a wheel, tire, or axle shaft.
You could rotate the tires front to back and see if the vibration moves.
If it does the problem is one of the tires or wheels.
If it stays in the front, its probably one of the axle shafts. It could also be a hub bearing or something loose in the suspension. But a loose suspension part would normally show up when you hit a bump rather than on a smooth road.

tires out of balance?

Likely a rotating part hitting a resonant frequency. It might be a universal joint on the drive shaft, a wheel out of balance or tire out of round. You might try lightly touching the brakes while maintaining the same speed. If it's something to do with tires or wheels, that would likely stop it. My first car would oscillate violently after hitting a bump in the road, due to a loose suspension part.

You have two unrelated problems. the power loss can be from a variety of things. What you first need to do with that is have a scan done (many parts stores do that free)...then if you have codes stored, you at least have some direction to go in with that.
The shaking is called death wobble and also has many causes. The most common are bad ball joints or tires that are worn sufficiently so as to not have enough foreward momentum to not react to side loading from bumps. The same tire can still generally pass inspection but is no longer useful on your vehicle (usually with around two thirty seconds of remaining tread measured at the wear bars). Any wear in any of the front end steering components or bushings can also cause wobble...sometimes it is a cumulative effect of slight wear in several places totaling an unacceptable amount of overall play. If you just had brake work or new tires installed, sometimes improper torquing of the wheels can also cause that. If you don't see anything obvious have an experienced jeep tech look at it. It can be dangerous and is nothing to ignore or wait on.

A few possibilities.... bent rim, broken steel belt in tire, or a wheel weight that keeps the tire/wheel combination in balance has fallen off. Not sure how big the bump was, so other options would be suspension related. I would check the tire and/or wheel first.

chances are your shocks are worn out completely. replace the shocks with a good quality set and take it for a drive. cheers.

Check your wheelbearings for play and your tierod ends for play,I'm sure one of these two are at fault.

The bumps do initiate the shaking. When my 2006 Ram 2500 4x4 started shaking, I had just had it aligned that morning. A month or so before that alignment, my passenger side outer tie-rod broke while driving down a rock road. I replaced it with a heavy duty MOOG tie-rod end. Anyway, the same day I had it aligned I was driving back home from a job and towing my bobcat behind me. I hit a bump and the truck did the "death wobble" with the front end shaking violently up and down in an alternating fashion (one tire in the air while one tire on the ground and then vice-versa). I changed the tires first (which were worn-out 305/75/17 mud tires). Since the day I bought the truck new in Jan. 2006, I've had larger tires on the truck than the tiny 235/75/17s that came with it and I've done a lot of heavy towing with it and never had a problem until this alignment was done at Sears. I;m still trying to figure out if it was the alignment specs that they used or if the problem coincidentally started that same day. I also changed the steering stabilizer. Neither the new tires nor the stabilizer/damper helped the problem. So I changed the other outer tie-rod end and the upper and lower ball joints (all MOOG with grease fittings). I turns out they were worn out. So, the truck no longer shakes violently up and down when I hit a bump. That problem seems to be in check. However, now when I hit a bump the truck's front end wobbles side-to-side. I can do a few things to recover from it. I can hit the brakes pretty hard and sudden (which can cause an accident on the interstate), or I can **** the steering wheel side-to-side a few times (from 10 o'clock to 2 o'clock) and that stops it immediately...until the next bump in the road. Also, if I let my foot off the accelerator just before hitting a bump and let the truck coast over it instead of power through it, sometimes the truck will ride over the bump without incident. I found out yesterday on a 5 1/2 hour road trip that if I did 80 to 90 miles per hour and powered through every road blemish, the truck rode fine...no shaking at all. I suppose the high speed forces the tires to stay straight when they hit a bump. Lastly, to confuse my problem solving attempts further, sometimes the truck rides like a cadillac (for an hour or so) at regular speeds and no matter what bumps I hit. Then without worning, the front end will loosen up and get that sloppy feeling again and the wobbling comes back at every bump...until the next time it feels like tightening up and driving right again. I have no idea what to do now. I'm going back to Sears today to have them check their alignment. Other than that, all I can think of is to change the rest of the steering components and check the steering box for malfunction. I hope someone can help all of us Dodge owners out off of the road tested info that I've just provided. Dodge doesn't seem to care to address the problems with their trucks front ends, and we need a solution before people get hurt or die. I was almost run over by an 18-wheeler trying to figure out how to handle the shake. I can't afford to buy another truck. So I need to fix this one so I can keep working. If anybody has a concrete solution to these problems, please let us know. I've read 20 different opinions from mechanics on these blogs, but nobody has said yet that they fixed someone's truck with these problems and have since heard from that customer and everything is still working fine. Opinions are helpful sometimes, but they're also confusing when they're conflicting.

Could be a number of things from ball joints to your pitman arm(arm that steers the tires). It dont sound like tire are way out of balance because yu said it only starts when you hit a bump. If it was me, Id crawl under the front end and start shaking different parts until I figured out what was loose. if its shaking that bad you should definitly be able to tell when you shake it.

Check the ball joints and cv axles this could cause the car to shake violently and most tire stores will check them for you for free.