MATHCOUNTS Mini #49 - Bases and Powers

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This video focuses on bases and powers.

Video by Art of Problem Solving's Richard Rusczyk, a MATHCOUNTS alum. Visit Art of Problem Solving for many more educational resources.
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Haha I completely forgot about "We did that earlier." Nice problems and clear explanations make an entertaining and great video, as always :D

_mstang
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What a *power*ful tool! Great video as always.

I remember that 2^30 one.

miamininja
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"And I don't like real pain" LOL

anonymous
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the last problem is like the collatze's conjecture

helo
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Wait wut? I thought that the answer to the last problem would be 8 because it is 7 powers of 2 plus the 1....?

funexperiments
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On the last problem why can't you just work backwards? starting from 1 you could only go to two and every other power of 2 is never one more than a square 

themaskedhoodedguy
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how did you convert 27 base 10 to 102 base 5? and is 27 an exponent and if so shouldnt it be to the right top of 10?

kharkhoreee
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how did u get 102 when converting 27 into base 5? cuz I got 12

narz
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What would happen with "0"???

SuperProwl