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Assumptions question (1/m^x,x>1,m=Infinity)


How do I simplify this:
1/m^x
when I know that x>1 and m is extremely large, so this term cancels
and becomes 0.
I'm thinking about something like:
Simplify[Limit[1/m^x,m->Infinity],x>1]
But I can't get math to figure out what I meant, I've tried about all
possible things with Simplify, Limit and Assumptions that I've realy
run out of ideas..
I'm realy desperate... BTW, I'm using mathematica 4.1 for linux.
Any help would be very much appreciated,
groetjes,
Hugo


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