document.write( "Question 1152301: Simplify cube root of 648x^14y^18 \n" ); document.write( "
Algebra.Com's Answer #774300 by Edwin McCravy(20056)\"\" \"About 
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\"root%283%2C648x%5E14y%5E18%29\"\r\n" );
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document.write( "Write the numerical coefficient as the cube of 6:\r\n" );
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document.write( "1. Divide each exponent of each base in the radicand, by the index of the root,\r\n" );
document.write( "2. Find the quotient and the remainder in each case.\r\n" );
document.write( "3. Write the base to the quotient power in front of the radical.\r\n" );
document.write( "4. Write the base to the remainder power inside the radical. \r\n" );
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document.write( "We begin with 63. The base is 6 and the exponent is 3. The index\r\n" );
document.write( "of the root is 3.  We divide the exponent 3 by the index 3 and get quotient 1\r\n" );
document.write( "with remainder 0.  So we write 61 in front of the radical, and the\r\n" );
document.write( "base 6 to the remainder power, 60 inside the radical:\r\n" );
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document.write( "\"6%5E1%2Aroot%283%2C6%5E0x%5E14y%5E18%29\"\r\n" );
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document.write( "Next we have x14. The base is x and the exponent is 14. The index\r\n" );
document.write( "of the root is 3.  We divide the exponent 14 by the index 3 and get quotient 4\r\n" );
document.write( "with remainder 2.  So we write x4 in front of the radical, and the\r\n" );
document.write( "base x to the remainder power, x2 inside the radical: \r\n" );
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document.write( "\"6%5E1x%5E4%2Aroot%283%2C6%5E0x%5E2y%5E18%29\"\r\n" );
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document.write( "Then we have y18. The base is y and the exponent is 18. The index\r\n" );
document.write( "of the root is 3.  We divide the exponent 18 by the index 3 and get quotient 6\r\n" );
document.write( "with remainder 0.  So we write y6 in front of the radical, and the\r\n" );
document.write( "base y to the remainder power, y0 inside the radical: \r\n" );
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document.write( "\"6%5E1x%5E4y%5E6%2Aroot%283%2C6%5E0x%5E2y%5E0%29\"\r\n" );
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document.write( "Now since anything to the 0 power is 1*, we can eliminate writing the 0 powers,\r\n" );
document.write( "and also the 1 exponent in the front.  So the final answer is:\r\n" );
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document.write( "\"6x%5E4y%5E6%2Aroot%283%2Cx%5E2%29\"\r\n" );
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document.write( "*except 00 which is undefined, which we did not run into.\r\n" );
document.write( "Edwin
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