document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200354>Question 200354</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need you help with  Evaluate. Ö[25a^12b^8c^12] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150640 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=150640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming you meant to say \"simplify\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%2Aa%5E12%2Ab%5E8%2Ac%5E12%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2Aa%5E12%2Ab%5E8%2Ac%5E12%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=sqrt%2825%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Ab%5E8%2Ac%5E12%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Ab%5E8%2Ac%5E12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E12 ALIGN=MIDDLE  ALT=\"a%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2\"   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=sqrt%2825%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Ab%5E2%2Ab%5E2%2Ab%5E2%2Ab%5E2%2Ac%5E12%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E8 ALIGN=MIDDLE  ALT=\"b%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Ab%5E2%2Ab%5E2%2Ab%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2Ab%5E2%2Ab%5E2%2Ab%5E2\"   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=sqrt%2825%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2%2Ab%5E2%2Ab%5E2%2Ab%5E2%2Ab%5E2%2Ac%5E2%2Ac%5E2%2Ac%5E2%2Ac%5E2%2Ac%5E2%2Ac%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E12 ALIGN=MIDDLE  ALT=\"c%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2%2Ac%5E2%2Ac%5E2%2Ac%5E2%2Ac%5E2%2Ac%5E2 ALIGN=MIDDLE  ALT=\"c%5E2%2Ac%5E2%2Ac%5E2%2Ac%5E2%2Ac%5E2%2Ac%5E2\"   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=sqrt%2825%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29 ALIGN=MIDDLE  ALT=\"sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%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=5%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   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=5%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   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=5%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab%2Ab%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   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=5%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab%2Ab%2Ac%2Ac%2Ac%2Ac%2Ac%2Ac ALIGN=MIDDLE  ALT=\"5%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab%2Ab%2Ac%2Ac%2Ac%2Ac%2Ac%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2 ALIGN=MIDDLE  ALT=\"c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"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=5a%5E6b%5E4c%5E6 ALIGN=MIDDLE  ALT=\"5a%5E6b%5E4c%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\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=sqrt%2825%2Aa%5E12%2Ab%5E8%2Ac%5E12%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2Aa%5E12%2Ab%5E8%2Ac%5E12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a%5E6b%5E4c%5E6 ALIGN=MIDDLE  ALT=\"5a%5E6b%5E4c%5E6\"   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=sqrt%2825%2Aa%5E12%2Ab%5E8%2Ac%5E12%29=5a%5E6b%5E4c%5E6 ALIGN=MIDDLE  ALT=\"sqrt%2825%2Aa%5E12%2Ab%5E8%2Ac%5E12%29=5a%5E6b%5E4c%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is non-negative.<BR>\n" );
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