document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171982>Question 1171982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am missing (or got a block for !) some very basic knowledge of exponents. \r<BR>\n" );
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document.write( "Question: X^(-2/3) = (1/9), solve for x\r<BR>\n" );
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document.write( "What I did: Raise the power of both L and R to -3/2 in order to get rid of the exponent of the variable X. Then the equation is\r<BR>\n" );
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document.write( "X^(-2/3)^(-3/2) = (1/9)^(-3/2) and it solves to X = +/- 27. Book says I got the right answer. \r<BR>\n" );
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document.write( "But it says while going through initial step of X^(-2/3)^(-3/2) = (1/9)^(-3/2)<BR>\n" );
document.write( "it wants me to add a +/- in front of the (1/9) as <BR>\n" );
document.write( "X^(-2/3)^(-3/2) = +/-(1/9)^(-3/2)\r<BR>\n" );
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document.write( "Why do I have to insert the +/- sign at this stage. Is it an accepted practice that you add +/- whenever you raise the power a negative fraction?....since it is going to require it anyway further down the steps?\r<BR>\n" );
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document.write( "Please help\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796891 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The reason is when you take a square root of both sides of an equation, you now need the +/- on one side or else information is lost.<br>\r<BR>\n" );
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document.write( "Example<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+-+2%29%5E2+=+25+ ALIGN=MIDDLE  ALT=\"+%28x+-+2%29%5E2+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28%28x+-+2%29%5E2%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28%28x+-+2%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%2825%29+ ALIGN=MIDDLE  ALT=\"+sqrt%2825%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (*)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+2+ ALIGN=MIDDLE  ALT=\"+x+-+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+ ALIGN=MIDDLE  ALT=\"+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+7+ ALIGN=MIDDLE  ALT=\"+x+=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-3+ ALIGN=MIDDLE  ALT=\"+x+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we only kept the positive root of both sides at (*), one answer would have been lost.<BR>\n" );
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document.write( "In your specific problem, raising to the -3/2  is a raise tox the -3 followed by  the square root operation (or square root followed by raise to the -3), so that's where the square root is creeping in.\r<BR>\n" );
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document.write( "Follow up: oh, I see what you mean.  I do not think the +/- needs to be added at that particular step, as you technically have not taken the sqrt(LHS) yet.  Once you write x by itself, then +/- is needed on RHS.   Remember though, it is the sqrt (multiple of 1/2 in the exponent) that is causing this need, not the fact that the exponent is negative.  \r<BR>\n" );
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document.write( "  </SPAN>\n" );
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