document.write( "Question 307213: 
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document.write( "How would I simplify this cubed problem? 3 ________________\r\n" );
document.write( "                                         \)-432x^17y^12\r\n" );
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Algebra.Com's Answer #219826 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "That's a clever way you came up with to make a cube\r\n" );
document.write( "root radical.  But you can put this\r\n" );
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document.write( "root(3,-432x^17y^12)\r\n" );
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document.write( "between triple brackets (three of these \"{\" in a row on the \r\n" );
document.write( "left and three of these \"}\" in a row on the right and you get\r\n" );
document.write( "this posted:\r\n" );
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document.write( "\"root%283%2C-432x%5E17y%5E12%29\"\r\n" );
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document.write( "Any odd root of a negative number is negative so\r\n" );
document.write( "we first of all take the negative sign out.  (You\r\n" );
document.write( "can only do this with odd roots, not even roots).\r\n" );
document.write( "So first we take out the negative sign:\r\n" );
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document.write( "\"-root%283%2C432x%5E17y%5E12%29\"\r\n" );
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document.write( "Next we break 432 into prime factors:\r\n" );
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document.write( "\"-root%283%2C2%5E4%2A3%5E3x%5E17y%5E12%29\"\r\n" );
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document.write( "Divide the index 3 into each exponent:\r\n" );
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document.write( "Divide index 3 into 4, the exponent of 2\r\n" );
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document.write( "  1\r\n" );
document.write( "3)4\r\n" );
document.write( "  3\r\n" );
document.write( "  1\r\n" );
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document.write( "The quotient is 1 and the remainder is 1\r\n" );
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document.write( "The quotient tells us what power of 2 comes out of the\r\n" );
document.write( "radical and the remainder tells us what power of 2 remains\r\n" );
document.write( "under the radical.  So \"2%5E1\" comes out in front of the\r\n" );
document.write( "radical and \"2%5E1\" remains under the radical:\r\n" );
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document.write( "\"-2%5E1%2Aroot%283%2C2%5E1%2A3%5E3x%5E17y%5E12%29\"\r\n" );
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document.write( "and of course we can erase the 1 exponents:\r\n" );
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document.write( "\"-2%2Aroot%283%2C2%2A3%5E3x%5E17y%5E12%29\"\r\n" );
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document.write( "Divide index 3 into 3, the exponent of 3\r\n" );
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document.write( "  1\r\n" );
document.write( "3)3\r\n" );
document.write( "  3\r\n" );
document.write( "  0 \r\n" );
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document.write( "The quotient is 1 and the remainder is 0\r\n" );
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document.write( "The quotient tells us what power of 3 comes out of the\r\n" );
document.write( "radical and the remainder tells us what power of x remains\r\n" );
document.write( "under the radical.  So \"3%5E1\" comes out in front of the\r\n" );
document.write( "radical and no power of 3 remains under the radical, or\r\n" );
document.write( "you can say \"3%5E0\" which is just 1 remains under the \r\n" );
document.write( "radical, but we don't even have to write it:\r\n" );
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document.write( "\"-2%2A3%2Aroot%283%2C2x%5E17y%5E12%29\"\r\n" );
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document.write( "Now we can multiply the -2 and the 3 in front of the radical\r\n" );
document.write( "and get:\r\n" );
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document.write( "\"-6%2Aroot%283%2C2x%5E17y%5E12%29\"\r\n" );
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document.write( "Divide index 3 into 17, the exponent of x\r\n" );
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document.write( "   5\r\n" );
document.write( "3)17\r\n" );
document.write( "  15\r\n" );
document.write( "   2 \r\n" );
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document.write( "The quotient is 5 and the remainder is 2\r\n" );
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document.write( "The quotient tells us what power of x comes out of the\r\n" );
document.write( "radical and the remainder tells us what power of x remains\r\n" );
document.write( "under the radical.  So \"x%5E5\" comes out in front of the\r\n" );
document.write( "radical and \"x%5E2\" remains under the radical:\r\n" );
document.write( "\r\n" );
document.write( "\"-6x%5E5%2Aroot%283%2C2x%5E2y%5E12%29\"\r\n" );
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document.write( "Divide index 3 into 12, the exponent of y\r\n" );
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document.write( "   4\r\n" );
document.write( "3)12\r\n" );
document.write( "  12\r\n" );
document.write( "   0 \r\n" );
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document.write( "The quotient is 4 and the remainder is 0\r\n" );
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document.write( "The quotient tells us what power of y comes out of the\r\n" );
document.write( "radical and the remainder tells us what power of y remains\r\n" );
document.write( "under the radical.  So \"y%5E4\" comes out in front of the\r\n" );
document.write( "radical and no power of y remains under the radical, or\r\n" );
document.write( "you can say \"x%5E0\" which is just 1 remains under the \r\n" );
document.write( "radical, but we don't even have to write it:\r\n" );
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document.write( "\"-6x%5E5y%5E4%2Aroot%283%2C2x%5E2%29\"\r\n" );
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document.write( "Edwin
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