document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262392>Question 262392</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this problem:\r<BR>\n" );
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document.write( "Write with positive exponents (3^-2 a^-2 b^5)over (c^-3 d^-4). \r<BR>\n" );
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document.write( "Thanks<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193327 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=193327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your expression is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E%28-2%29%2Aa%5E%28-2%29%2Ab%5E5%29%2F%28c%5E%28-3%29%2Ad%5E%28-4%29%29 ALIGN=MIDDLE  ALT=\"%283%5E%28-2%29%2Aa%5E%28-2%29%2Ab%5E5%29%2F%28c%5E%28-3%29%2Ad%5E%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "in general, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28-b%29 ALIGN=MIDDLE  ALT=\"a%5E%28-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa%5Eb ALIGN=MIDDLE  ALT=\"1%2Fa%5Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F3%5E2%29%2A%281%2Fa%5E2%29%2A%28b%5E5%29%29%2F%28%281%2Fc%5E3%29%2A%281%2Fd%5E4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this can be simplified to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E5%2F%283%5E2%2Aa%5E2%29%29%2F%281%2F%28c%5E3%2Ad%5E4%29%29 ALIGN=MIDDLE  ALT=\"%28b%5E5%2F%283%5E2%2Aa%5E2%29%29%2F%281%2F%28c%5E3%2Ad%5E4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if we multiply this by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%5E3%2Ad%5E4%29%2F%28c%5E3%2Ad%5E4%29 ALIGN=MIDDLE  ALT=\"%28c%5E3%2Ad%5E4%29%2F%28c%5E3%2Ad%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29%29%2F1%29 ALIGN=MIDDLE  ALT=\"%28%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29%29%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we confirm by substituting values for a,b,c,d in both the original equation and the final equation to see if we get the same answer.\r<BR>\n" );
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document.write( "we will let:\r<BR>\n" );
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document.write( "a = 2<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "c = 4<BR>\n" );
document.write( "d = 5\r<BR>\n" );
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document.write( "original equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E%28-2%29%2Aa%5E%28-2%29%2Ab%5E5%29%2F%28c%5E%28-3%29%2Ad%5E%28-4%29%29 ALIGN=MIDDLE  ALT=\"%283%5E%28-2%29%2Aa%5E%28-2%29%2Ab%5E5%29%2F%28c%5E%28-3%29%2Ad%5E%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substituting, this becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E%28-2%29%2A2%5E%28-2%29%2A3%5E5%29%2F%284%5E%28-3%29%2A5%5E%28-4%29%29 ALIGN=MIDDLE  ALT=\"%283%5E%28-2%29%2A2%5E%28-2%29%2A3%5E5%29%2F%284%5E%28-3%29%2A5%5E%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 270,000\r<BR>\n" );
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document.write( "final equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substituting, this becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%5E5%2A4%5E3%2A5%5E4%29%2F%283%5E2%2A2%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28%283%5E5%2A4%5E3%2A5%5E4%29%2F%283%5E2%2A2%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 270,000\r<BR>\n" );
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document.write( "since they both equal the same value, the simplification is good.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E%28-2%29%2Aa%5E%28-2%29%2Ab%5E5%29%2F%28c%5E%28-3%29%2Ad%5E%28-4%29%29 ALIGN=MIDDLE  ALT=\"%283%5E%28-2%29%2Aa%5E%28-2%29%2Ab%5E5%29%2F%28c%5E%28-3%29%2Ad%5E%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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