document.write( "Question 594115: Express radical 54x^7 in simplest raadical form \n" ); document.write( "
Algebra.Com's Answer #376635 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"sqrt%2854x%5E7%29\"\r\n" );
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document.write( "Write 54 as 2·27 and then as 21·33, and\r\n" );
document.write( "indicate the understood index of the root as 2\r\n" );
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document.write( "\"root%282%2C2%5E1%2A3%5E3%2Ax%5E7%29\"\r\n" );
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document.write( "Rules for \"root%28N%2CB%5EM%2A%22%28OTHER_FACTORS_IF_ANY%29%22%29\"\r\n" );
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document.write( "1. If M is less than N, then leave it as it is.\r\n" );
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document.write( "2. If M can be divided evenly by N, then it equals \r\n" );
document.write( "\"matrix%282%2C1%2C%22%22%2CB%5E%28M%2FN%29%29%2A%22%22\"\"root%28N%2C%22%28OTHER_FACTORS_IF_ANY%29%22%29\"\r\n" );
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document.write( "3. If M is greater than N, then do this division\r\n" );
document.write( "where Q is the quotient and R is the remainder \r\n" );
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document.write( "       Q\r\n" );
document.write( "     N)M\r\n" );
document.write( "       ...\r\n" );
document.write( "        R  \r\n" );
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document.write( "Then it equals:\r\n" );
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document.write( "\"B%5EQ%2A%22%22\"\"root%28N%2CB%5ER%2A%22%28OTHER_FACTORS_IF_ANY%29%22%29\"\r\n" );
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document.write( "\"root%284%2C+x%5E3y%5E5z%5E8%29\"\r\n" );
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document.write( "\"root%282%2C2%5E1%2A3%5E3%2Ax%5E7%29\"\r\n" );
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document.write( "For the 21, since 1 is less than 2, we use rule 1 and do nothing \r\n" );
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document.write( "For the 33, since the exponent 3 is greater than the index 2,\r\n" );
document.write( "we use rule 3 and do this division:\r\n" );
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document.write( "       1 \r\n" );
document.write( "     2)3\r\n" );
document.write( "       2\r\n" );
document.write( "       1\r\n" );
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document.write( "\"3%5E1%2Aroot%282%2C2%5E1%2A3%5E1%2Ax%5E7%29\"\r\n" );
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document.write( "For the x7, since 7 is greater than 2, we use rule 3\r\n" );
document.write( "and do this division:\r\n" );
document.write( "        \r\n" );
document.write( "       3 \r\n" );
document.write( "     2)7\r\n" );
document.write( "       6\r\n" );
document.write( "       1\r\n" );
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document.write( "and write:\r\n" );
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document.write( "\"3%5E1x%5E3%2Aroot%282%2C2%5E1%2A3%5E1x%5E1%29\" and dispose of the 1 exponents:\r\n" );
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document.write( "\"3x%5E3%2Aroot%282%2C2%2A3x%29\"\r\n" );
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document.write( "We can also multiply the 2 by the 3 and dispose of the 2 index and \r\n" );
document.write( "we end up with:\r\n" );
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document.write( "\"3x%5E3%2Asqrt%286x%29\"\r\n" );
document.write( "     \r\n" );
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document.write( "Edwin
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