document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201790>Question 201790</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Multiply: sqrt (x)^1/3 (sqrt (3x^2)^1/3 - sqrt (81x^2)^1/3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152040 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=152040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your formula looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%29%29%5E%28%281%2F3%29%29+%2A+%28%28sqrt%283%2Ax%5E2%29%29%5E%28%281%2F3%29%29+-+%28sqrt+%2881%2Ax%5E2%29%29%5E%28%281%2F3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > if I understand it correctly.<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"x%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > this formula can be rewritten as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E%281%2F2%29%29%5E%281%2F3%29+%2A+%28%28%283%2Ax%5E2%29%5E%281%2F2%29%29%5E%281%2F3%29+-+%28%2881%2Ax%5E2%29%5E%281%2F2%29%29%5E%281%2F3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since by the rules of exponents <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Ea%29%5Eb ALIGN=MIDDLE  ALT=\"%28x%5Ea%29%5Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28a%2Ab%29 ALIGN=MIDDLE  ALT=\"x%5E%28a%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this formula can be rewritten as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E%281%2F6%29+%2A+%28%283%2Ax%5E2%29%5E%281%2F6%29+-+%2881%2Ax%5E2%29%5E%281%2F6%29%29%29 ALIGN=MIDDLE  ALT=\"+x%5E%281%2F6%29+%2A+%28%283%2Ax%5E2%29%5E%281%2F6%29+-+%2881%2Ax%5E2%29%5E%281%2F6%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Ab%29%5Ec ALIGN=MIDDLE  ALT=\"%28a%2Ab%29%5Ec\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Ec%2Ab%5Ec ALIGN=MIDDLE  ALT=\"a%5Ec%2Ab%5Ec\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this formula can be rewritten as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F6%29%2A%28%283%5E%281%2F6%29%2Ax%5E%281%2F3%29%29+-+%2881%5E%281%2F6%29%2Ax%5E%281%2F3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"x%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a common factor, it can be factored out to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F6%29%2Ax%5E%281%2F3%29%2A%283%5E%281%2F6%29-81%5E%281%2F6%29%29 ALIGN=MIDDLE  ALT=\"x%5E%281%2F6%29%2Ax%5E%281%2F3%29%2A%283%5E%281%2F6%29-81%5E%281%2F6%29%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=x%5E%281%2F2%29%2A%283%5E%281%2F6%29-81%5E%281%2F6%29%29 ALIGN=MIDDLE  ALT=\"x%5E%281%2F2%29%2A%283%5E%281%2F6%29-81%5E%281%2F6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which i do not believe can be simplified any further, so I reduced the constants to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.879146868+%2A+x%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"-.879146868+%2A+x%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to prove the answer is correct, then take any value of x and solve the original equation and then solve the reduced equation.  you should get the same answer.<BR>\n" );
document.write( "I did it using a value of x = 4, 12, and 27.<BR>\n" );
document.write( "You can use any value you wish if you want to take the time to prove it to yourself.<BR>\n" );
document.write( " </SPAN>\n" );
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