SOLUTION: Find the smallest natural number to be multiplied with 72000 so that the product is a 5th power of an integer

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Question 882938: Find the smallest natural number to be multiplied with 72000 so that the product is a 5th power of an integer
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
72000=2%5E6%2A3%2A2%2A5%5E3 if you multiply by 3%5E3%2A5%5E2 then you will have 5th powers of 3 and 5. If you multiply by 2%5E4 you will then have 2%5E10=4%5E5.
So then the multiplier is 2%5E4%2A3%5E3%2A5%5E2=16%2A27%2A25=10800
72000%2A10800=4%5E5%2A3%5E5%2A5%5E5
777600000=%283%2A4%2A5%29%5E5
777600000=%2860%29%5E5