document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=716671>Question 716671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the expression. Express your answer so that only positive.\r<BR>\n" );
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document.write( "(4x^-1y^1/3)^3/2 divided by (xy)^3/2\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #440072 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=440072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E%28-1%29y%5E%281%2F3%29%29%5E%283%2F2%29%2F%28xy%29%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"%284x%5E%28-1%29y%5E%281%2F3%29%29%5E%283%2F2%29%2F%28xy%29%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the rule:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ab%29%5En+=+a%5En%2Ab%5En ALIGN=MIDDLE  ALT=\"a%2Ab%29%5En+=+a%5En%2Ab%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in both the numerator and denominator we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E%283%2F2%29%2A%28x%5E%28-1%29%29%5E%283%2F2%29%29%2A%28y%5E%281%2F3%29%29%5E%283%2F2%29%29%29%2F%28x%5E%283%2F2%29%2Ay%5E%283%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Next we'll use the power of a power rule in the numerator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E%283%2F2%29%2A%28x%5E%28-3%2F2%29%29%2A%28y%5E%281%2F2%29%29%29%2F%28x%5E%283%2F2%29%2Ay%5E%283%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we'll simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"4%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the rule <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28m%2Fn%29+=+%28root%28n%2C+a%29%29%5Em ALIGN=MIDDLE  ALT=\"a%5E%28m%2Fn%29+=+%28root%28n%2C+a%29%29%5Em\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%283%2F2%29+=+%28root%282%2C+4%29%29%5E3+=+2%5E3+=+8 ALIGN=MIDDLE  ALT=\"4%5E%283%2F2%29+=+%28root%282%2C+4%29%29%5E3+=+2%5E3+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now our expression is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2A%28x%5E%28-3%2F2%29%29%2A%28y%5E%281%2F2%29%29%29%2F%28x%5E%283%2F2%29%2Ay%5E%283%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we'll use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Em%2Fa%5En+=+a%5E%28%28m-n%29%29 ALIGN=MIDDLE  ALT=\"a%5Em%2Fa%5En+=+a%5E%28%28m-n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > rule to divide the x's and y's:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A%28x%5E%28%28-3%2F2%29-%283%2F2%29%29%29%2A%28y%5E%28%281%2F2%29-%283%2F2%29%29%29 ALIGN=MIDDLE  ALT=\"8%2A%28x%5E%28%28-3%2F2%29-%283%2F2%29%29%29%2A%28y%5E%28%281%2F2%29-%283%2F2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting the fractions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A%28x%5E%28%28-6%2F2%29%29%29%2A%28y%5E%28%28-2%2F2%29%29%29 ALIGN=MIDDLE  ALT=\"8%2A%28x%5E%28%28-6%2F2%29%29%29%2A%28y%5E%28%28-2%2F2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplify to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A%28x%5E%28%28-3%29%29%29%2A%28y%5E%28%28-1%29%29%29 ALIGN=MIDDLE  ALT=\"8%2A%28x%5E%28%28-3%29%29%29%2A%28y%5E%28%28-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a simplified expression. Assuming that the \"only positive\" in your post means \"using only positive exponents\" then we have a little more work to do. Using the rule <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28%28-n%29%29+=+1%2Fa%5En ALIGN=MIDDLE  ALT=\"a%5E%28%28-n%29%29+=+1%2Fa%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A%281%2Fx%5E3%29%2A%281%2Fy%5E1%29 ALIGN=MIDDLE  ALT=\"8%2A%281%2Fx%5E3%29%2A%281%2Fy%5E1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F%28x%5E3%2Ay%29 ALIGN=MIDDLE  ALT=\"8%2F%28x%5E3%2Ay%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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