document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126393>Question 126393</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 #92597 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=92597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sqrt{180x^{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 \left(180x^{4}\right)^{\frac{1}{2}}\"> Convert the expression from radical notation to exponent notation. Remember <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{\textrm{A}}=\sqrt[2]{\textrm{A}}=\textrm{A}^{\frac{1}{2}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left((180)^1x^4\right)^{\frac{1}{2}}\"> Rewrite 180 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5E1 ALIGN=MIDDLE  ALT=\"180%5E1\"   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 (180)^{1\left(\frac{1}{2}\right)}x^{4\left(\frac{1}{2}\right)}\"> Now distribute the exponent Now distribute the outer exponent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to each exponent in the parenthesis. Remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Ey%29%5Ez=x%5E%28y%2Az%29 ALIGN=MIDDLE  ALT=\"%28x%5Ey%29%5Ez=x%5E%28y%2Az%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 (180)^{\frac{1}{2}}x^{\frac{4}{2}}\"> Now multiply the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (180)^{\frac{1}{2}}x^{2}\"> Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{180}x^{2}\"> Now convert back to radical notation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 6\sqrt{5}x^{2}\"> Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29 ALIGN=MIDDLE  ALT=\"sqrt%28180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>\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%28180x%5E4%29 ALIGN=MIDDLE  ALT=\"sqrt%28180x%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"6x%5E2%2Asqrt%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=sqrt%28180x%5E4%29=6x%5E2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%28180x%5E4%29=6x%5E2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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