If you mean by the "power of prayer", you asked for a certain request, and it happened.............I'm not sure i see that very often.
The way i look at it, though, i do believe it has power.
" 6 Do not be anxious about anything, but in everything, by prayer and petition, with thanksgiving, present your requests to God. 7 And the peace of God, which transcends all understanding, will guard your hearts and your minds in Christ Jesus. " -- I believe that i have experienced this, that praying about things about which I am anxious and worrying, does often result in an experience of the peace of God here spoken of.
I know also that when i pray for others, my love and concern for them is increased. It takes me out of my own little world of hurt and problems, and forces me to see behind the eyes of those around me, and care more about their sufferings. -- (and I'm not implying at all that those who don't believe in prayer don't care about others....... )