document.write( "Question 837613: Can't figure this out for the life of me.Thanks in advance\r
\n" ); document.write( "\n" ); document.write( "(3m^2/3-4m^-1/3) factor out m^-1/3 \n" ); document.write( "
Algebra.Com's Answer #504658 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"matrix%282%2C1%2C%22%22%2C+3m%5E%282%2F3%29-4m%5E%28-1%2F3%29%29\" \r\n" );
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document.write( "We can easily factor \"matrix%282%2C1%2C%22%22%2Cm%5E%28-1%2F3%29%29\" out of the second\r\n" );
document.write( "term.  So the only hitch is in factoring \"matrix%282%2C1%2C%22%22%2Cm%5E%28-1%2F3%29%29\" out of the first term.  \r\n" );
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document.write( "Let's let P be the power of m that we leave inside the parentheses\r\n" );
document.write( "when we factor \"matrix%282%2C1%2C%22%22%2Cm%5E%28-1%2F3%29%29\" out of the first term.\r\n" );
document.write( "That is, suppose P is such that the original expression factors \r\n" );
document.write( "like this:\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C+m%5E%28-1%2F3%29%283m%5EP-4%29%29\"\r\n" );
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document.write( "Now let's multiply that back out by adding exponents of m \r\n" );
document.write( "on the first term:\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C+3m%5E%28-1%2F3%2BP%29-4m%5E%28-1%2F3%29%29\"\r\n" );
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document.write( "That has to equal the power of m in the first term of the original:\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C+3m%5E%282%2F3%29-4m%5E%28-1%2F3%29%29\" \r\n" );
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document.write( "So we must have \"-1%2F3%2BP=2%2F3\".  Solve that for P\r\n" );
document.write( "                \"P=2%2F3%2B1%2F3\"\r\n" );
document.write( "                \"P=3%2F3\"\r\n" );
document.write( "                \"P=1\"\r\n" );
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document.write( "So we replace P by 1 in\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C+m%5E%28-1%2F3%29%283m%5EP-4%29%29\"\r\n" );
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document.write( "and get:\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C+m%5E%28-1%2F3%29%283m%5E1-4%29%29\"\r\n" );
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document.write( "or just:\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C+m%5E%28-1%2F3%29%283m-4%29%29\"\r\n" );
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document.write( "Edwin
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