document.write( "Question 393123: Please walk me thru this problem:\r
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\n" ); document.write( "\n" ); document.write( "7x/ ∛ 4x y^5 (cube root of 4xy to 5th power) \n" ); document.write( "
Algebra.Com's Answer #279078 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Break the denominator down into prime factors:\r\n" );
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document.write( "We now must decide what factors the denominator would need in order \r\n" );
document.write( "for it to become a perfect cube.  We need three or a multiple of \r\n" );
document.write( "three of each factor:\r\n" );
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document.write( "We have 2*2, which is two factors, so we need one more factor of 2\r\n" );
document.write( "so we'll have three factors of 2.\r\n" );
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document.write( "We have x, which is one factor, so we need two more factors of x\r\n" );
document.write( "so we'll have three factors of x.\r\n" );
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document.write( "We have y*y*y*y*y, which is five factors, so we need one more factor of y\r\n" );
document.write( "so we'll have a multiple of three, that is, six factors of y.\r\n" );
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document.write( "So we create another cube root which has what we need in it, one\r\n" );
document.write( "factor of 2, two factors of x and one factor of y.  That is, we\r\n" );
document.write( "create this cube root:\r\n" );
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document.write( "\"root%283%2C2%2Ax%2Ax%2Ay%29\"\r\n" );
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document.write( "Then we place it over itself so that the value will be 1.\r\n" );
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document.write( "\"root%283%2C2%2Ax%2Ax%2Ay%29%2Froot%283%2C2%2Ax%2Ax%2Ay%29\"\r\n" );
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document.write( "And we can now multiply it by the original expression without\r\n" );
document.write( "changing its value since we are actually only multiplying by 1.\r\n" );
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document.write( "\"%287x%29%2Froot%283%2C2%2A2%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay%29\"\"%22%22%2A%22%22\"\"root%283%2C2%2Ax%2Ax%2Ay%29%2Froot%283%2C2%2Ax%2Ax%2Ay%29\"\r\n" );
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document.write( "Now we multiply under the radicals on the bottom:\r\n" );
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document.write( "Now we group the like factors in the bottom into groups of three:\r\n" );
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document.write( "Now we write each group of three as the cube of a single factor:\r\n" );
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document.write( "\"%287x%2Aroot%283%2C2%2Ax%2Ax%2Ay%29%29%2Froot%283%2C2%5E3%2Ax%5E3%2Ay%5E3%2Ay%5E3%29\"\r\n" );
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document.write( "Now take individual cube roots:\r\n" );
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document.write( "\"%287x%2Aroot%283%2C2%2Ax%2Ax%2Ay%29%29%2F%282%2Ax%2Ay%2Ay%29\"\r\n" );
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document.write( "Write the \"x%2Ax\" in the top as \"x%5E2\" and the \"y%2Ay\" in\r\n" );
document.write( "the bottom as \"y%5E2\"\r\n" );
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document.write( "\"%287x%2Aroot%283%2C2x%5E2y%29%29%2F%282xy%5E2%29\"\r\n" );
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document.write( "You can perhaps figure out a shorter way than this, but this method\r\n" );
document.write( "will always work.  Do them this way and I think you will figure out \r\n" );
document.write( "a shortcut after doing a few this longer but easier to follow way.\r\n" );
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document.write( "Edwin
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