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Traditional theology states that Jesus was all man and all God (or God incarnate) at the same time (yeah...that's a brain buster.) So he had traits that are ascribed to God like omniscience, omnipresence, and omnipotence. He clearly humbled himself to walk among us, laying his powers aside. At times, however, he took them up showing his omniscience (knowing the thoughts of the Pharisee's hearts) and omnipotence (walking on water amongst others).

Take from that what you will, just explaining the traditional theology .
R.C. Sproul (a modern, well respected thologian) explains this here. One thing of note is that many of the miracles Jesus performed are ascribed to "the Father" and not Jesus himself. Like when a prophet would perform a miracle (say calling fire from heaven), it is not the prophet's power but God's power initiated by the faithfulness of the prophet. Though certainly Jesus had the power, He chose to not use it and instead rely on His relationship to the Father.
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-Jeff
Rome did not create a great empire by having meetings; they did it by killing all those who opposed them.