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Imagine the product of $20^{50}$ and $50^{20}$ written as an integer in standard form. how many zeros will be found at the end of this number?

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Do you mean 20^{50} and 50^{20}? –  Amzoti Dec 16 '12 at 18:41
What have you tried? A zero at the end of this product comes from a factor of $10=2\cdot 5$ in it. So, how many $10$ can you produce? –  lhf Dec 16 '12 at 18:42
This question has nothing to do with either integer-lattices or integer-programming so I've retagged it. (Of course, if you can think of more appropriate tags, feel free to change the tags I've chosen.) –  Martin Sleziak Dec 16 '12 at 18:48
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HINT: $20^{50}\cdot50^{20}=\left(2\cdot10\right)^{50}\left(5\cdot10\right)^{20}=2^{50}\cdot10^{50}\cdot5^{20}\cdot10^{20}=2^{50}\cdot5^{20}\cdot10^{50+20}$. How many zeroes will you get from $10^{50+20}$? How many more from $2^{50}\cdot5^{20}$?

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