document.write( "Question 881765: Hi,\r
\n" ); document.write( "\n" ); document.write( "What is the reciprocal of the (cube root of 81)?
\n" ); document.write( "So if drawn out, it would have 3 as the index, and 81 as the radicand.\r
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Algebra.Com's Answer #532468 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
First simplify\r
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\n" ); document.write( "\n" ); document.write( "\"root%283%2C81%29+=+root%283%2C27%2A3%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"root%283%2C81%29+=+root%283%2C27%29%2Aroot%283%2C3%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"root%283%2C81%29+=+3%2Aroot%283%2C3%29\"\r
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\n" ); document.write( "\n" ); document.write( "Then take the reciprocal. Make sure to rationalize the denominator.\r
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\n" ); document.write( "\n" ); document.write( "\"1%2F%28root%283%2C81%29%29+=+1%2F%283%2Aroot%283%2C3%29%29\"\r
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\n" ); document.write( "\n" ); document.write( " Multiply top and bottom by 2 copies of \"root%283%2C3%29\" to rationalize the denominator.\r
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\n" ); document.write( "\n" ); document.write( "\"1%2F%28root%283%2C81%29%29+=+%28root%283%2C3%2A3%29%29%2F%283%2Aroot%283%2C3%2A3%2A3%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"1%2F%28root%283%2C81%29%29+=+%28root%283%2C9%29%29%2F%283%2Aroot%283%2C27%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"1%2F%28root%283%2C81%29%29+=+%28root%283%2C9%29%29%2F%283%2A3%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"1%2F%28root%283%2C81%29%29+=+%28root%283%2C9%29%29%2F%289%29\"\r
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\n" ); document.write( "\n" ); document.write( "So the reciprocal of \"root%283%2C81%29\" is \"%28root%283%2C9%29%29%2F%289%29\"
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