document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171801>Question 171801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i can not figure this problem out:\r<BR>\n" );
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document.write( "sqrt 2^109 x sqrt x^306 x sqrt x^11  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126913 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=126913\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: remember, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{x^2}=\left(x^{\frac{1}{2}}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{2^{109}}\cdot\sqrt{x^{306}}\cdot\sqrt{x^{11}}\"> 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{2\cdot2^{108}}\cdot\sqrt{x^{306}}\cdot\sqrt{x\cdot x^{10}}\"> Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28109%29 ALIGN=MIDDLE  ALT=\"2%5E%28109%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%5E%28108%29 ALIGN=MIDDLE  ALT=\"2%2A2%5E%28108%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%2811%29=x%2Ax%5E%2810%29 ALIGN=MIDDLE  ALT=\"x%5E%2811%29=x%2Ax%5E%2810%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{2}\cdot\sqrt{2^{108}}\cdot\sqrt{x^{306}}\cdot\sqrt{x\cdot x^{10}}\"> Break up <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{2\cdot2^{108}}\"> to get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{2}\cdot\sqrt{2^{108}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{2}\cdot\sqrt{2^{108}}\cdot\sqrt{x^{306}}\cdot\sqrt{x}\cdot\sqrt{x^{10}}\"> Break up <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{x\cdot x^{10}}\"> to get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{x}\cdot\sqrt{x^{10}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{2}\cdot\left(2^{108}\right)^{\frac{1}{2}}\cdot\left(x^{306}\right)^{\frac{1}{2}}\cdot\sqrt{x}\cdot\left(x^{10}\right)^{\frac{1}{2}}\">  Convert from radical notation to exponential notation (see note above).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{2}\cdot\left(2^{\frac{108}{2}}\right)\cdot\left(x^{\frac{306}{2}}\right)\cdot\sqrt{x}\cdot\left(x^{\frac{10}{2}}\right)\"> Multiply the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{2}\cdot\left(2^{54}\right)\cdot\left(x^{153}\right)\cdot\sqrt{x}\cdot\left(x^{5}\right)\"> Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2^{54}\left(x^{153}\right)\cdot\left(x^{5}\right)\sqrt{2x}\"> Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2^{54}x^{158}\sqrt{2x}\"> Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28153%29 ALIGN=MIDDLE  ALT=\"x%5E%28153%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%285%29 ALIGN=MIDDLE  ALT=\"x%5E%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28153%29%2Ax%5E%285%29=x%5E%28153%2B5%29=x%5E%28158%29 ALIGN=MIDDLE  ALT=\"x%5E%28153%29%2Ax%5E%285%29=x%5E%28153%2B5%29=x%5E%28158%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{2^{109}}\cdot\sqrt{x^{306}}\cdot\sqrt{x^{11}}\"> simplifies to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2^{54}x^{158}\sqrt{2x}\"> \r<BR>\n" );
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document.write( "In other words <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{2^{109}}\cdot\sqrt{x^{306}}\cdot\sqrt{x^{11}}=2^{54}x^{158}\sqrt{2x}\"> where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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