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While you are trying to generate power, you must keep your balance through your swing. Smoothly transferring your weight forward while generating power from your legs will allow for maximum torque upon impact with the ball. The more torque you generate, the more energy will be transferred to the ball. Whether you are dealing with an inside swing or an outside swing, it is important to keep your hands close to your body. Most of your swing is generated in your hands and wrists. If your hands are extended your bat speed will slow and your power will drop. The palm of your dominant (top) hand should remain facing upwards through contact in order to drive through the ball. Don't over-swing, or try to put any extra power into it. Most of the power in a swing is generated through your hips and wrists. Allow that power to flow through your body smoothly. Trying to swing extra hard will harm rather than help you. Trying to "muscle" through the ball will usually result in your body tightening up, which compromises your natural kinetic chain and prevents your wrists from snapping into your swing as quickly. Light muscles are fast muscles. Tight muscles are slow muscles. Properly following through is important for multiple reasons. Not only will it help you to add all-important distance generating backspin to the ball, but it will help point out any flaws in your swing. In most cases, you want your hands to finish high which ensures that the bat head stays through the hitting zone as long as possible.
Transfer your weight smoothly as you swing. Keep your hands in. Control your swing. Follow through.