document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126506>Question 126506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify\r<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 #92678 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=92678\">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%2C162a%5E10b%5E5%29%2Froot%283%2C6a%5E8b%5E4%29 ALIGN=MIDDLE  ALT=\"root%283%2C162a%5E10b%5E5%29%2Froot%283%2C6a%5E8b%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "First let's simplify the numerator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C162a%5E10b%5E5%29 ALIGN=MIDDLE  ALT=\"root%283%2C162a%5E10b%5E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt[3]{162a^{10}b^5}\"> Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt[3]{162}\sqrt[3]{a^{10}}\sqrt[3]{b^{5}}\"> Break up the roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Aroot%283%2C6%29%2Aa%5E3%2Aroot%283%2Ca%29%2Ab%2Aroot%283%2Cb%5E2%29 ALIGN=MIDDLE  ALT=\"3%2Aroot%283%2C6%29%2Aa%5E3%2Aroot%283%2Ca%29%2Ab%2Aroot%283%2Cb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C162%29 ALIGN=MIDDLE  ALT=\"root%283%2C162%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Aroot%283%2C6%29 ALIGN=MIDDLE  ALT=\"3%2Aroot%283%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Ca%5E10%29 ALIGN=MIDDLE  ALT=\"root%283%2Ca%5E10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2Aroot%283%2Ca%29 ALIGN=MIDDLE  ALT=\"a%5E3%2Aroot%283%2Ca%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cb%5E5%29 ALIGN=MIDDLE  ALT=\"root%283%2Cb%5E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Aroot%283%2Cb%5E2%29 ALIGN=MIDDLE  ALT=\"b%2Aroot%283%2Cb%5E2%29\"   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=3a%5E3b%2Aroot%283%2C6ab%5E2%29 ALIGN=MIDDLE  ALT=\"3a%5E3b%2Aroot%283%2C6ab%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply and combine the roots\r<BR>\n" );
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document.write( "So  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C162a%5E10b%5E5%29 ALIGN=MIDDLE  ALT=\"root%283%2C162a%5E10b%5E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%5E3b%2Aroot%283%2C6ab%5E2%29 ALIGN=MIDDLE  ALT=\"3a%5E3b%2Aroot%283%2C6ab%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's simplify the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C6a%5E8b%5E4%29 ALIGN=MIDDLE  ALT=\"root%283%2C6a%5E8b%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt[3]{6a^8b^4}\"> Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt[3]{6}\sqrt[3]{a^8}\sqrt[3]{b^{4}}\"> Break up the roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C6%29%2Aa%5E2%2Aroot%283%2Ca%5E2%29%2Ab%2Aroot%283%2Cb%29 ALIGN=MIDDLE  ALT=\"root%283%2C6%29%2Aa%5E2%2Aroot%283%2Ca%5E2%29%2Ab%2Aroot%283%2Cb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Ca%5E8%29 ALIGN=MIDDLE  ALT=\"root%283%2Ca%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Aroot%283%2Ca%5E2%29 ALIGN=MIDDLE  ALT=\"a%5E2%2Aroot%283%2Ca%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cb%5E4%29 ALIGN=MIDDLE  ALT=\"root%283%2Cb%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Aroot%283%2Cb%29 ALIGN=MIDDLE  ALT=\"b%2Aroot%283%2Cb%29\"   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=a%5E2b%2Aroot%283%2C6a%5E2b%29 ALIGN=MIDDLE  ALT=\"a%5E2b%2Aroot%283%2C6a%5E2b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply and combine the roots\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C6a%5E8b%5E4%29 ALIGN=MIDDLE  ALT=\"root%283%2C6a%5E8b%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2b%2Aroot%283%2C6a%5E2b%29 ALIGN=MIDDLE  ALT=\"a%5E2b%2Aroot%283%2C6a%5E2b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So now our expression becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a%5E3b%2Aroot%283%2C6ab%5E2%29%29%2F%28a%5E2b%2Aroot%283%2C6a%5E2b%29%29 ALIGN=MIDDLE  ALT=\"%283a%5E3b%2Aroot%283%2C6ab%5E2%29%29%2F%28a%5E2b%2Aroot%283%2C6a%5E2b%29%29\"   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=%283a%2Aroot%283%2C6ab%5E2%29%29%2F%28root%283%2C6a%5E2b%29%29 ALIGN=MIDDLE  ALT=\"%283a%2Aroot%283%2C6ab%5E2%29%29%2F%28root%283%2C6a%5E2b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a%5E3b%29%2F%28a%5E2b%29 ALIGN=MIDDLE  ALT=\"%283a%5E3b%29%2F%28a%5E2b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a ALIGN=MIDDLE  ALT=\"3a\"   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=3a%2Aroot%283%2C%286ab%5E2%29%2F%286a%5E2b%29%29 ALIGN=MIDDLE  ALT=\"3a%2Aroot%283%2C%286ab%5E2%29%2F%286a%5E2b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2Aroot%283%2Cb%2Fa%29 ALIGN=MIDDLE  ALT=\"3a%2Aroot%283%2Cb%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286ab%5E2%29%2F%286a%5E2b%29 ALIGN=MIDDLE  ALT=\"%286ab%5E2%29%2F%286a%5E2b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fa ALIGN=MIDDLE  ALT=\"b%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C162a%5E10b%5E5%29%2Froot%283%2C6a%5E8b%5E4%29 ALIGN=MIDDLE  ALT=\"root%283%2C162a%5E10b%5E5%29%2Froot%283%2C6a%5E8b%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2Aroot%283%2Cb%2Fa%29 ALIGN=MIDDLE  ALT=\"3a%2Aroot%283%2Cb%2Fa%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%2C162a%5E10b%5E5%29%2Froot%283%2C6a%5E8b%5E4%29=3a%2Aroot%283%2Cb%2Fa%29 ALIGN=MIDDLE  ALT=\"root%283%2C162a%5E10b%5E5%29%2Froot%283%2C6a%5E8b%5E4%29=3a%2Aroot%283%2Cb%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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