document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148124>Question 148124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C40a%5E3b%5E6c%5E8%29 ALIGN=MIDDLE  ALT=\"root%283%2C40a%5E3b%5E6c%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108513 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=108513\">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=root%283%2C40a%5E3b%5E6c%5E8%29 ALIGN=MIDDLE  ALT=\"root%283%2C40a%5E3b%5E6c%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C8%2A5a%5E3b%5E6c%5E8%29 ALIGN=MIDDLE  ALT=\"root%283%2C8%2A5a%5E3b%5E6c%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A5 ALIGN=MIDDLE  ALT=\"8%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice how 8 is a perfect cube (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=2%5E3 ALIGN=MIDDLE  ALT=\"8=2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >). \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C8%2A5a%5E3b%5E3%2Ab%5E3c%5E8%29 ALIGN=MIDDLE  ALT=\"root%283%2C8%2A5a%5E3b%5E3%2Ab%5E3c%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E6 ALIGN=MIDDLE  ALT=\"b%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E3%2Ab%5E3 ALIGN=MIDDLE  ALT=\"b%5E3%2Ab%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Once again, notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E3 ALIGN=MIDDLE  ALT=\"b%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfect cube. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C8%2A5a%5E3b%5E3%2Ab%5E3c%5E8%29 ALIGN=MIDDLE  ALT=\"root%283%2C8%2A5a%5E3b%5E3%2Ab%5E3c%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E8 ALIGN=MIDDLE  ALT=\"c%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E3%2Ac%5E3%2Ac%5E2 ALIGN=MIDDLE  ALT=\"c%5E3%2Ac%5E3%2Ac%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Once again, notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E3 ALIGN=MIDDLE  ALT=\"c%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfect cube. \r<BR>\n" );
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document.write( "I'm breaking the expression into perfect cubes so that when I take the cube root of these cubes, I'll be left with the expression itself. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E3 ALIGN=MIDDLE  ALT=\"b%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfect cube, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cb%5E3%29=b ALIGN=MIDDLE  ALT=\"root%283%2Cb%5E3%29=b\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Also, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E3 ALIGN=MIDDLE  ALT=\"c%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfect cube, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cc%5E3%29=c ALIGN=MIDDLE  ALT=\"root%283%2Cc%5E3%29=c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C8%29%2Aroot%283%2C5%29%2Aroot%283%2Ca%5E3%29%2Aroot%283%2Cb%5E3%29%2Aroot%283%2Cb%5E3%29%2Aroot%283%2Cc%5E3%29%2Aroot%283%2Cc%5E3%29%2Aroot%283%2Cc%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C5%29%2Aa%2Ab%2Ab%2Ac%2Ac%2Aroot%283%2Cc%5E2%29 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C5%29%2Aa%2Ab%2Ab%2Ac%2Ac%2Aroot%283%2Cc%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the cube root of the perfect cubes to get just the base of the expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab%5E2c%5E2%2Aroot%283%2C5c%5E2%29 ALIGN=MIDDLE  ALT=\"2ab%5E2c%5E2%2Aroot%283%2C5c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Recombine any roots leftover and multiply\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C40a%5E3b%5E6c%5E8%29 ALIGN=MIDDLE  ALT=\"root%283%2C40a%5E3b%5E6c%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab%5E2c%5E2%2Aroot%283%2C5c%5E2%29 ALIGN=MIDDLE  ALT=\"2ab%5E2c%5E2%2Aroot%283%2C5c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C40a%5E3b%5E6c%5E8%29=2ab%5E2c%5E2%2Aroot%283%2C5c%5E2%29 ALIGN=MIDDLE  ALT=\"root%283%2C40a%5E3b%5E6c%5E8%29=2ab%5E2c%5E2%2Aroot%283%2C5c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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