document.write( "Question 882938: Find the smallest natural number to be multiplied with 72000 so that the product is a 5th power of an integer \n" ); document.write( "

Algebra.Com's Answer #533186 by Fombitz(32388) $\"\"$ $\"About$

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$\"72000=2%5E6%2A3%2A2%2A5%5E3\"$ 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 $\"2%5E10=4%5E5\"$ .
\n" ); document.write( "So then the multiplier is $\"2%5E4%2A3%5E3%2A5%5E2=16%2A27%2A25=10800\"$
\n" ); document.write( " $\"72000%2A10800=4%5E5%2A3%5E5%2A5%5E5\"$
\n" ); document.write( " $\"777600000=%283%2A4%2A5%29%5E5\"$
\n" ); document.write( " $\"777600000=%2860%29%5E5\"$ \r
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