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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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closed as off-topic by 900 sit-ups a day, T. Bongers, Gina, Adam Hughes, Tomás Aug 1 '14 at 0:42

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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

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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Actually, how many (for $2^{50} \cdot 5^{50}$)? – Shahar May 12 '14 at 3:58

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