document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77895>Question 77895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how can i simplify by combining like terms?\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 #56053 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=56053\">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=%2863%5E%28-2%29%29%2A%2828%5E5%29%2A7 ALIGN=MIDDLE  ALT=\"%2863%5E%28-2%29%29%2A%2828%5E5%29%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The negative exponent can be changed to a positive exponent if the 63 is moved to a denominator.<BR>\n" );
document.write( "This would make the problem:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F63%5E2%29%2A%2828%5E5%29%2A7 ALIGN=MIDDLE  ALT=\"%281%2F63%5E2%29%2A%2828%5E5%29%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now factor the 63 into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2A7%29 ALIGN=MIDDLE  ALT=\"%289%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the 28 into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A7 ALIGN=MIDDLE  ALT=\"4%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substitute these into the<BR>\n" );
document.write( "expression to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%289%2A7%29%5E2%29%2A%28%284%2A7%29%5E5%29%2A7 ALIGN=MIDDLE  ALT=\"%281%2F%289%2A7%29%5E2%29%2A%28%284%2A7%29%5E5%29%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "by the power rule of exponents, the terms inside the parentheses each get raised to the<BR>\n" );
document.write( "power associated with the brackets.  This converts the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%289%5E2%2A7%5E2%29%2A%284%5E5%29%2A%287%5E5%29%2A7 ALIGN=MIDDLE  ALT=\"1%2F%289%5E2%2A7%5E2%29%2A%284%5E5%29%2A%287%5E5%29%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in the numerator multiply the terms containing 7 by adding exponents (remember that 7<BR>\n" );
document.write( "is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%5E1%29 ALIGN=MIDDLE  ALT=\"%287%5E1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%289%5E2%2A7%5E2%29%2A+%284%5E5%29%2A%287%5E6%29 ALIGN=MIDDLE  ALT=\"1%2F%289%5E2%2A7%5E2%29%2A+%284%5E5%29%2A%287%5E6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "divide the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E2 ALIGN=MIDDLE  ALT=\"7%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the denominator into the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E6 ALIGN=MIDDLE  ALT=\"7%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the numerator by subtracting<BR>\n" );
document.write( "the exponents to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E%286-2%29+=+7%5E4 ALIGN=MIDDLE  ALT=\"7%5E%286-2%29+=+7%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This reduces the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%289%5E2%29%2A+%284%5E5%29%2A%287%5E4%29+=+%28%284%5E5%29%2A%287%5E4%29%29%2F9%5E2 ALIGN=MIDDLE  ALT=\"1%2F%289%5E2%29%2A+%284%5E5%29%2A%287%5E4%29+=+%28%284%5E5%29%2A%287%5E4%29%29%2F9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "there are no more factors in the numerator that are common with factors in the denominator.<BR>\n" );
document.write( "You could, if you wish, factor the 4 of the first term into the numerator into 2*2 and<BR>\n" );
document.write( "the 9 in the denominator into 3*3 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%282%2A2%29%5E5%29%2A7%5E4%29%2F%283%2A3%29%5E2 ALIGN=MIDDLE  ALT=\"%28%28%282%2A2%29%5E5%29%2A7%5E4%29%2F%283%2A3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which would expand to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%5E5%29%2A%282%5E5%29%2A7%5E4%29%2F%283%5E2%2A3%5E2%29+ ALIGN=MIDDLE  ALT=\"%28%282%5E5%29%2A%282%5E5%29%2A7%5E4%29%2F%283%5E2%2A3%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "but that doesn't accomplish much.  Or you could multiply everything out to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2458624%2F81 ALIGN=MIDDLE  ALT=\"2458624%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to see how to work this problem.<BR>\n" );
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