How does God answer prayer without affecting free will?

Since God doesn’t interfere with free will, how then does He answer prayer? I’m just trying to understand how the power of prayer works. It just seems the only way to change any event is to directly interfere but this is against God’s word, so how then would He answer a prayer? Just curious on other’s thoughts..

Free choice can only be made on the condition that the Creator does not show himself to us and thus we are created in a condition of His absence from our perception. If we had a perception of Him we would be unable to stop our self from cleaving to the pleasure that emanates from Him thus the condition of complete separation without the influence of His force gives us the chance to independently arrive at the desire to approach Him and cleave to Him.

Prayers that ask for a change in events that are happening in the world or to fix problems are not the ones that get a response because these are things He created specifically to prepare us for turning to Him and request to approach Him. The Creator will answer your prayer if it relates to spiritual advancement towards understanding and knowing Him. This kind of prayer asks for changes within you that will lead to spiritual ascent. This ascent leads to happiness and closeness to the Creator and in this regard the Creator can and will do anything for you. This is the reason prayer is called "the work of the heart" because we work to direct all our desire to be for the Creator. I hope this helps.

Here is a video on prayer to explain further:

http://www.kabbalah.info/engkab/kabbalah-video-clips/prayer

And here is vieo with a very good explanation on the complex topic of free will:

http://www.kabbalah.info/engkab/kabbalah-video-clips/free-will