document.write( "Question 212871: Please help me.
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Algebra.Com's Answer #160829 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Please help me.
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document.write( "Subtract the exponents of the \"x\"'s\r\n" );
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document.write( "\"root%284%2C5x%5E6y%5E3%2F27%29\"\r\n" );
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document.write( "Write the \"27\"  as \"3%2A3%2A3\" and\r\n" );
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document.write( "\"root%284%2C%285x%5E6y%5E3%29%2F%283%2A3%2A3%29%29\"\r\n" );
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document.write( "Now take individual fourth roots of the\r\n" );
document.write( "top and bottom.\r\n" );
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document.write( "\"root%284%2C%285x%5E6y%5E3%29%29%2Froot%284%2C%283%2A3%2A3%29%29%29\"\r\n" );
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document.write( "The denominator has only three factors of\r\n" );
document.write( "3.  It needs one more 3, so it will be a \r\n" );
document.write( "perfect fourth power, and come out of the\r\n" );
document.write( "fourth root radical.\r\n" );
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document.write( "So we multiply top and bottom of the fraction\r\n" );
document.write( "by \"red%283%29\".\r\n" );
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document.write( "\"root%284%2C%28+5x%5E6y%5E3%2Ared%283%29+%29%2F%283%2A3%2A3%2Ared%283%29%29%29\"\r\n" );
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document.write( "Now that there are 4 factors of 3 in the\r\n" );
document.write( "denominator, we can write the denominator as\r\n" );
document.write( "\"3%5E4\" and simplify the numerator:\r\n" );
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document.write( "\"root%284%2C%2815x%5E6y%5E3+%29%2F%283%5E4%29%29\" \r\n" );
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document.write( "Now we take individual fourth roots of the\r\n" );
document.write( "top and bottom:\r\n" );
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document.write( "\"root%284%2C%2815x%5E6y%5E3+%29%29%2Froot%284%2C3%5E4%29%29\"\r\n" );
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document.write( "And since the bottom is the 4th root of\r\n" );
document.write( "a 4th power we just take away the 4th root\r\n" );
document.write( "radical and the 4th power.\r\n" );
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document.write( "\"root%284%2C%2815x%5E6y%5E3+%29%29%2F3\"\r\n" );
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document.write( "The factor \"x%5E6\" is a case of an exponent 6\r\n" );
document.write( "under a radical being as large or larger than, in\r\n" );
document.write( "this case larger than, the index of the radical, 4.\r\n" );
document.write( "That means it will simplify further.\r\n" );
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document.write( "So we write \"x%5E6\" as \"red%28x%5E4x%5E2%29\" so the \"x%5E4\"\r\n" );
document.write( "will come out of the fourth root radical, like the 4\r\n" );
document.write( "3's did above in the denominator.\r\n" );
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document.write( "\"root%284%2C%2815red%28x%5E4x%5E2%29y%5E3+%29%29%2F3\"\r\n" );
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document.write( "Now you can take \"x%5E4\" out of the radical and\r\n" );
document.write( "just have \"x\" in front of the radical on top:\r\n" );
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document.write( "\"x%2Aroot%284%2C%2815x%5E2y%5E3+%29%29%2F3\"  \r\n" );
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document.write( "Edwin
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