document.write( "Question 814009: Simplify 8m^4sqrt(100m^9p^4)\r
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Algebra.Com's Answer #490083 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"8m%5E4sqrt%28100m%5E9p%5E4%29\"\r\n" );
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document.write( "The index of a square root is 2, and write 100 as 102: \r\n" );
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document.write( "\"8m%5E4\"\"%22%22%2A%22%22\"\"root%282%2C10%5E2m%5E9p%5E4%29\"\r\n" );
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document.write( "10 and p already has exponents that can\r\n" );
document.write( "be divided evenly by index 2.  But m doesn't. We write\r\n" );
document.write( "m9 as m8m1 so that m8 will have as large as possible an exponent divisible by 2.\r\n" );
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document.write( "\"8m%5E4\"\"%22%22%2A%22%22\"\"root%282%2C10%5E2m%5E8m%5E1p%5E4%29\"\r\n" );
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document.write( "We take 102 out of the square root as\r\n" );
document.write( "10 with exponent 1 by dividing the index\r\n" );
document.write( "into the exponent 2 of 10.\r\n" );
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document.write( "We take m8 out of the square root as\r\n" );
document.write( "m with exponent 4 by dividing the index\r\n" );
document.write( "2 into the exponent 8 of x.\r\n" );
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document.write( "We take p4 out of the square root as\r\n" );
document.write( "p with exponent 2 by dividing the index 2\r\n" );
document.write( "into the exponent 4 of p.\r\n" );
document.write( " And we have\r\n" );
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document.write( "\"8m%5E4%2A10%5E1m%5E4p%5E2\"\"%22%22%2A%22%22\"\"root%282%2Cm%5E1%29\"\r\n" );
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document.write( "\"8m%5E8%2A10p%5E2\"\"%22%22%2A%22%22\"\"root%282%2Cm%29\"\r\n" );
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document.write( "\"80m%5E8p%5E2\"\"sqrt%28m%29\"\r\n" );
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document.write( "Edwin
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