document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187173>Question 187173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help on this equation.<BR>\n" );
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document.write( "(6a^3b)(8a^4b^2)   over.....<BR>\n" );
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document.write( "30a^3b^2<BR>\n" );
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document.write( "thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140303 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=140303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286a%5E3b%29%288a%5E4b%5E2%29+ ALIGN=MIDDLE  ALT=\"%286a%5E3b%29%288a%5E4b%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=%286a%5E3b%29%288a%5E4b%5E2%29+ ALIGN=MIDDLE  ALT=\"%286a%5E3b%29%288a%5E4b%5E2%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=%286%2A8%29%28a%5E3%2Aa%5E4%29%28b%2Ab%5E2%29+ ALIGN=MIDDLE  ALT=\"%286%2A8%29%28a%5E3%2Aa%5E4%29%28b%2Ab%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%28a%5E3%2Aa%5E4%29%28b%2Ab%5E2%29+ ALIGN=MIDDLE  ALT=\"48%28a%5E3%2Aa%5E4%29%28b%2Ab%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 6 and 8 to get 48\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%28a%5E%283%2B4%29%29%28b%5E%281%2B2%29%29+ ALIGN=MIDDLE  ALT=\"48%28a%5E%283%2B4%29%29%28b%5E%281%2B2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the exponents to multiply the monomials.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48a%5E7%2Ab%5E3 ALIGN=MIDDLE  ALT=\"48a%5E7%2Ab%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286a%5E3b%29%288a%5E4b%5E2%29=48a%5E7%2Ab%5E3 ALIGN=MIDDLE  ALT=\"%286a%5E3b%29%288a%5E4b%5E2%29=48a%5E7%2Ab%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286a%5E3b%29%288a%5E4b%5E2%29%29%2F%2830a%5E3b%5E2%29+ ALIGN=MIDDLE  ALT=\"%28%286a%5E3b%29%288a%5E4b%5E2%29%29%2F%2830a%5E3b%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "simplifies to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2848a%5E7%2Ab%5E3%29%2F%2830a%5E3b%5E2%29+ ALIGN=MIDDLE  ALT=\"%2848a%5E7%2Ab%5E3%29%2F%2830a%5E3b%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=%282%2A2%2A2%2A2%2A3%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab%29%2F%282%2A3%2A5%2Aa%2Aa%2Aa%2Ab%2Ab%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Expand. \r<BR>\n" );
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document.write( "Note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48a%5E7b%5E3=2%2A2%2A2%2A2%2A3%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab ALIGN=MIDDLE  ALT=\"48a%5E7b%5E3=2%2A2%2A2%2A2%2A3%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > (there are 7 a's and 3 b's) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30a%5E3b%5E2=2%2A3%2A5%2Aa%2Aa%2Aa%2Ab%2Ab ALIGN=MIDDLE  ALT=\"30a%5E3b%5E2=2%2A3%2A5%2Aa%2Aa%2Aa%2Ab%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > (there are 3 a's and 3 b's)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%282%29%2A2%2A2%2A2%2Ahighlight%283%29%2Ahighlight%28a%29%2Ahighlight%28a%29%2Ahighlight%28a%29%2Aa%2Aa%2Aa%2Aa%2Ahighlight%28b%29%2Ahighlight%28b%29%2Ab%29%2F%28highlight%282%29%2Ahighlight%283%29%2A5%2Ahighlight%28a%29%2Ahighlight%28a%29%2Ahighlight%28a%29%2Ahighlight%28b%29%2Ahighlight%28b%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%282%29%2A2%2A2%2A2%2Across%283%29%2Across%28a%29%2Across%28a%29%2Across%28a%29%2Aa%2Aa%2Aa%2Aa%2Across%28b%29%2Across%28b%29%2Ab%29%2F%28cross%282%29%2Across%283%29%2A5%2Across%28a%29%2Across%28a%29%2Across%28a%29%2Across%28b%29%2Across%28b%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2A2%2A2%2Aa%2Aa%2Aa%2Aa%2Ab%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%282%2A2%2A2%2Aa%2Aa%2Aa%2Aa%2Ab%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288a%5E4b%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%288a%5E4b%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Regroup and multiply.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2848a%5E7b%5E3%29%2F%2830a%5E3b%5E2%29 ALIGN=MIDDLE  ALT=\"%2848a%5E7b%5E3%29%2F%2830a%5E3b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288a%5E4b%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%288a%5E4b%29%2F%285%29\"   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=%28%286a%5E3b%29%288a%5E4b%5E2%29%29%2F%2830a%5E3b%5E2%29+ ALIGN=MIDDLE  ALT=\"%28%286a%5E3b%29%288a%5E4b%5E2%29%29%2F%2830a%5E3b%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288a%5E4b%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%288a%5E4b%29%2F%285%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=%28%286a%5E3b%29%288a%5E4b%5E2%29%29%2F%2830a%5E3b%5E2%29=%288a%5E4b%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%28%286a%5E3b%29%288a%5E4b%5E2%29%29%2F%2830a%5E3b%5E2%29=%288a%5E4b%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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