document.write( "Question 906529: Hi, I'm stuck on the following problem. Would you help me solve it, please?\r
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\n" ); document.write( "\n" ); document.write( "I got 256 as an answer by raising both sides to the (5/2) power, but my online homework system is saying that's only 50% correct. Did I forget another answer or important step?
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Algebra.Com's Answer #549927 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Hi, I'm stuck on the following problem. Would you help me solve it, please?\r
\n" ); document.write( "\n" ); document.write( "Directions: Solve the equation and check all proposed answers.
\n" ); document.write( "\"matrix%282%2C1%2C%22%22%2C+%28x-13%29%5E%282%2F5%29=9%29+\"\r
\n" ); document.write( "\n" ); document.write( "I got 256 as an answer by raising both sides to the (5/2) power, but my online homework system is saying that's only 50% correct. Did I forget another answer or important step?
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document.write( "Don't raise both sides to the 'reciprocal power' ever again. Raise both sides to\r\n" );
document.write( "the 'denominator power' instead. I know you were taught to raise both sides to\r\n" );
document.write( "the 'reciprocal power' when you first started taking algebra.  But don't\r\n" );
document.write( "do that anymore because it sometimes causes you to lose solutions in more\r\n" );
document.write( "advanced problems like this one which is more advanced than the ones you had\r\n" );
document.write( "when you learned to use the reciprocal power. Raise both sides to the\r\n" );
document.write( "denominator power, (the fifth power) not the reciprocal power.\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C+%28%28x-13%29%5E%282%2F5%29%29%5E5=9%5E5%29+\"\r\n" );
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document.write( "\"%28x-13%29%5E2=9%5E5\"\r\n" );
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document.write( "Now use the principle of square roots:\r\n" );
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document.write( "\"x-13=%22%22%2B-sqrt%289%5E5%29\"\r\n" );
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document.write( "Write 9 as 3²\r\n" );
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document.write( "\"x-13=%22%22%2B-sqrt%28%283%5E2%29%5E5%29\"\r\n" );
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document.write( "Multiply the exponents\r\n" );
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document.write( "\"x-13=%22%22+%2B-+sqrt%283%5E10%29\"\r\n" );
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document.write( "\"x-13=%22%22+%2B-+3%5E5\"\r\n" );
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document.write( "\"x-13=%22%22+%2B-+243\"\r\n" );
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document.write( "\"x=13+%2B-+243\"\r\n" );
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document.write( "So there are 2 solutions.\r\n" );
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document.write( "Using the +,\r\n" );
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document.write( "\"x=13%2B243\"\r\n" );
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document.write( "\"x=256\"\r\n" );
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document.write( "Using the -\r\n" );
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document.write( "\"x=13-243\"\r\n" );
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document.write( "\"x=-230\"\r\n" );
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document.write( "That's the other answer.  Don't raise both sides to the reciprocal power\r\n" );
document.write( "ever again.  Just raise to the denominator power. \r\n" );
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document.write( "Edwin
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