When I zoom useing my panasonic lumix DMC-FX01 it turns off

Have you had problems when you turn it on and off from scratch before? It sounds like you have a problem with the lense extension. Now if you are lucky, it's just a bit of dirt in there and the best cure (I know, it sounds horrible) is to put the end of a shop-vac over the lense when it's closed and it will probably **** the obstruction out. If you are less lucky, the problem is with the gearing inside and in the middle of the luck-vs-effort range it could just have been bashed, in which case, you can try and push it back into alignment but be careful with it (he says, after he hit his last one with a large lump of wood to put it back).

Good luck :)