document.write( "Question 460172: Simplify the expression, and rationalize the denominator if appropriate.\r
\n" ); document.write( "\n" ); document.write( "Cube root of \"2x%5E4y%5E4%2F9x\" \n" ); document.write( "
Algebra.Com's Answer #315643 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
\"root%283%2C%282x%5E4y%5E4%29%2F%289x%29%29\"
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document.write( "First we cancel the x in the bottom into the x⁴\r\n" );
document.write( " in the top getting x³ in the top\r\n" );
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document.write( "\"root%283%2C%282x%5E3y%5E4%29%2F%289%29%29\"\r\n" );
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document.write( "Next we break the cube root of a quotient \r\n" );
document.write( "into the quotient of two cube roots:\r\n" );
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document.write( "\"root%283%2C2x%5E3y%5E4%29%2Froot%283%2C9%29\"\r\n" );
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document.write( "Next we want to get rid of the cube root on\r\n" );
document.write( "the bottom. It contains 9 = 3*3.  Let's write\r\n" );
document.write( "9 as 3*3\r\n" );
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document.write( "\"root%283%2C2x%5E3y%5E4%29%2Froot%283%2C3%2A3%29\"\r\n" );
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document.write( "We can make that 3*3 into the perfect cube 3*3*3 \r\n" );
document.write( "or 3³ by multiplying it by 3, so we multiply the \r\n" );
document.write( "entire fraction by \"root%283%2C3%29%2Froot%283%2C3%29\"\r\n" );
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document.write( "Now we multiply numerators and denominators by \r\n" );
document.write( "multiplying under radicals:\r\n" );
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document.write( "\"root%283%2C2%2A3x%5E3y%5E4%29%2Froot%283%2C3%2A3%2A3%29\"\r\n" );
document.write( "  \r\n" );
document.write( "\"root%283%2C6x%5E3y%5E4%29%2Froot%283%2C3%5E3%29\"\r\n" );
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document.write( "Now the denominator becomes just 3 and we write\r\n" );
document.write( "the y⁴in the numerator as y³y:\r\n" );
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document.write( "\"root%283%2C6x%5E3y%5E3y%29%2F3\"\r\n" );
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document.write( "Finally we take the x³y³ out of the radical in \r\n" );
document.write( "the numerator and put xy in front:\r\n" );
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document.write( "\"%28xy%2Aroot%283%2C6y%29%29%2F3\"\r\n" );
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document.write( "Edwin

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