document.write( "Question 46690: simplify the radical . assume that all variables represent positive numbers.\r
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Algebra.Com's Answer #30925 by AnlytcPhil(1806)\"\" \"About 
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simplify the radical . assume that all variables \r\n" );
document.write( "represent positive numbers. 3rd root of 343 x to\r\n" );
document.write( "the 4th power y to the 5th power\r\n" );
document.write( "  _______\r\n" );
document.write( "³Ö343x4y5\r\n" );
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document.write( "Break everything down to primes\r\n" );
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document.write( "343 = 7·7·7\r\n" );
document.write( "x4 = x·x·x·x\r\n" );
document.write( "y5 = y·y·y·y·y\r\n" );
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document.write( "So we have this\r\n" );
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document.write( "³Ö7·7·7·x·x·x·x·y·y·y·y·y\r\n" );
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document.write( "Since it's a cube root (i.e. \"third root\"),\r\n" );
document.write( "we use parentheses to group into all possible\r\n" );
document.write( "groups of three like factors each:\r\n" );
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document.write( "³Ö(7·7·7)·(x·x·x)·x·(y·y·y)·y·y\r\n" );
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document.write( "Now each of the groups of three can be rewritten\r\n" );
document.write( "as a cube.  (7·7·7) = 7³, (x·x·x) = x³, and\r\n" );
document.write( "(y·y·y) = y³,  So now we have:\r\n" );
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document.write( "³Ö7³·x³·x·y³·y·y\r\n" );
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document.write( "Now take the cube roots of the cubes under the\r\n" );
document.write( "radical. That is take the cubes outside in front\r\n" );
document.write( "of the radical without the cube exponent.  What\r\n" );
document.write( "did not group stays under the radical.\r\n" );
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document.write( "7·x·y·³Öx·y·y\r\n" );
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document.write( "or simplifying,\r\n" );
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document.write( "7xy·³Öxy² \r\n" );
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document.write( "Edwin
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