document.write( "Question 550915: simplify cube root 54 x^10 please show steps and help me to understand why the steps work \n" ); document.write( "
Algebra.Com's Answer #359224 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The root is cube root which is the 3rd root, so we want to get\r\n" );
document.write( "as many exponens under it as possible that can be divided evenly by 3.\r\n" );
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document.write( "We break up 54 as 27·2, then as 9·3·2 and then as 3·3·3·2 and then as 3³·2\r\n" );
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document.write( "So instead of 54 we write 3³·2\r\n" );
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document.write( "That has one exponent that is divisible by 3.\r\n" );
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document.write( "Now lets break x10 up as x9·x1, because\r\n" );
document.write( "9 is divisible by 3.  So we write this:\r\n" );
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document.write( "\"root%283%2C3%5E3%2A2x%5E9x%5E1%29\"\r\n" );
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document.write( "Now we can divide the two exponents 3 and 9 by 3 getting 1 and 3,\r\n" );
document.write( "and take them out of the radical and put the resulting exponentials\r\n" );
document.write( "out in front of the radical:\r\n" );
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document.write( "\"3%5E1%2Ax%5E3%2Aroot%283%2C2x%5E1%29\"\r\n" );
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document.write( "Erase the 1 exponents:\r\n" );
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document.write( "\"3x%5E3%2Aroot%283%2C2x%29\"\r\n" );
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document.write( "Edwin
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