document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=325203>Question 325203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> express in fractional form with positive exponents only\r<BR>\n" );
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document.write( "(6x^-3 y^4)^-2  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #232986 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=232986\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-a%29 ALIGN=MIDDLE  ALT=\"x%5E%28-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%5Ea ALIGN=MIDDLE  ALT=\"1%2Fx%5Ea\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then your equation is transformed as follows:\r<BR>\n" );
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document.write( "Start with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2Ax%5E%28-3%29+%2A+y%5E4%29%5E%28-2%29 ALIGN=MIDDLE  ALT=\"%286%2Ax%5E%28-3%29+%2A+y%5E4%29%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2F+%28%286%2Ax%5E%28-3%29+%2A+y%5E4%29%5E2%29 ALIGN=MIDDLE  ALT=\"1+%2F+%28%286%2Ax%5E%28-3%29+%2A+y%5E4%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This then becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2F+%28%286%2Ay%5E4%2Fx%5E3%29%5E2%29 ALIGN=MIDDLE  ALT=\"1+%2F+%28%286%2Ay%5E4%2Fx%5E3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax%5E%28-3%29 ALIGN=MIDDLE  ALT=\"6%2Ax%5E%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fx%5E3 ALIGN=MIDDLE  ALT=\"6%2Fx%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Fb%29%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Fb%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Fb%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Fb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2F+%28%286%2Ay%5E4%2Fx%5E3%29%5E2%29 ALIGN=MIDDLE  ALT=\"1+%2F+%28%286%2Ay%5E4%2Fx%5E3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2F+%28%286%2Ay%5E4%29%5E2%2F%28x%5E3%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"1+%2F+%28%286%2Ay%5E4%29%5E2%2F%28x%5E3%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28a%2Fb%29 ALIGN=MIDDLE  ALT=\"1%2F%28a%2Fb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2Fa%29 ALIGN=MIDDLE  ALT=\"%28b%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2F+%28%286%2Ay%5E4%29%5E2%2F%28x%5E3%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"1+%2F+%28%286%2Ay%5E4%29%5E2%2F%28x%5E3%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%29%5E2%2F%286%2Ay%5E4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E3%29%5E2%2F%286%2Ay%5E4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Eb%29%5Ec ALIGN=MIDDLE  ALT=\"%28a%5Eb%29%5Ec\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28b%2Ac%29 ALIGN=MIDDLE  ALT=\"a%5E%28b%2Ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Ab%29%5Ec+=+a%5Ec%2Ab%5Ec ALIGN=MIDDLE  ALT=\"%28a%2Ab%29%5Ec+=+a%5Ec%2Ab%5Ec\"   DISABLED_style= \"max-width:90%; height:auto;\" > then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%29%5E2%2F%286%2Ay%5E4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E3%29%5E2%2F%286%2Ay%5E4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E6%29%2F%286%5E2%2Ay%5E8%29 ALIGN=MIDDLE  ALT=\"%28x%5E6%29%2F%286%5E2%2Ay%5E8%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=%28x%5E6%29%2F%2836%2Ay%5E8%29 ALIGN=MIDDLE  ALT=\"%28x%5E6%29%2F%2836%2Ay%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If we transformed the equation correctly, then the original equation is equivalent to the final equation.\r<BR>\n" );
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document.write( "We can confirm that by taking any values for x and any values for y and seeing if both equations give us the same answer.\r<BR>\n" );
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document.write( "Let x = 4 and y = 5.\r<BR>\n" );
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document.write( "The original equation gives you a value of 000291271\r<BR>\n" );
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document.write( "The final equation gives you a value of .000291271\r<BR>\n" );
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document.write( "Since both equations give you the same answer, then the transposition can be assumed to be good.\r<BR>\n" );
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document.write( "If you really wanted to make sure, you would pick two other numbers at random and see if both equations give you the same answer.\r<BR>\n" );
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document.write( "No real reason to here so we can assume we're good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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