document.write( "Question 69787: How do you solve:
\n" ); document.write( "x^-2=9
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Algebra.Com's Answer #49752 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Your problem is:\r
\n" ); document.write( "\n" ); document.write( "\"x%5E%28-2%29+=+9\"\r
\n" ); document.write( "\n" ); document.write( "The negative exponent means that the term raised to that negative value can be changed
\n" ); document.write( "into a fraction having 1 as the numerator and the term with a positive exponent as the
\n" ); document.write( "denominator. Easier to show by an example than to explain it.\r
\n" ); document.write( "\n" ); document.write( "Think \"I can change \"x%5E%28-2%29\" into \"x%5E2%29\" by making \"%28x%5E2%29\" the denominator
\n" ); document.write( "of a fraction that has 1 as its numerator.\" When you do that your problem becomes:\r
\n" ); document.write( "\n" ); document.write( "\"1%2Fx%5E2+=+9\"\r
\n" ); document.write( "\n" ); document.write( "Then you can eliminate the denominator if you multiply both sides by \"x%5E2\"\r
\n" ); document.write( "\n" ); document.write( "If you do that multiplication on the left side you have a fraction that has \"x%5E2\"
\n" ); document.write( "in both the numerator and denominator. This is equivalent to 1. On the right side the multiplication results in \"9%2Ax%5E2\" and the problem becomes:\r
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\n" ); document.write( "\n" ); document.write( "\"+1+=+9x%5E2\"\r
\n" ); document.write( "\n" ); document.write( "Dividing both sides by 9 gives:\r
\n" ); document.write( "\n" ); document.write( "\"1%2F9+=+x%5E2\"\r
\n" ); document.write( "\n" ); document.write( "Now just take the square root of both sides. Notice that \"sqrt%281%2F9%29+=+1%2F3\" because
\n" ); document.write( "\"%281%2F3%29%2A%281%2F3%29+=+%281%2F9%29\". Also notice that both the positive and negative forms
\n" ); document.write( "of \"1%2F3\" are needed because when either is squared they produce a positive value
\n" ); document.write( "of \"1%2F9\"\r
\n" ); document.write( "\n" ); document.write( "The two answers to this problem are:\r
\n" ); document.write( "\n" ); document.write( "\"1%2F3+=+x\" and \"-1%2F3+=+x\"\r
\n" ); document.write( "\n" ); document.write( "You can check this by putting each of these answers (positive and negative) one at a time
\n" ); document.write( "into the equation:\r
\n" ); document.write( "\n" ); document.write( "\"1%2Fx%5E2+=+9\"\r
\n" ); document.write( "\n" ); document.write( "and see that with these values the left side of the equation equals 9.\r
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