document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82505>Question 82505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign.\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 #59821 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=59821\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets say you had \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2Aroot%283%2Cx%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Aroot%283%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "how would you simplify this? Well since we have a square root and a cube root, we cannot mix the two expressions. In order to simplify, you would have to raise everything to the 6th power like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%29%2Aroot%283%2Cx%29%29%5E6 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%29%2Aroot%283%2Cx%29%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Ax%5E2 ALIGN=MIDDLE  ALT=\"x%5E3%2Ax%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=x%5E5 ALIGN=MIDDLE  ALT=\"x%5E5\"   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=root%286%2Cx%5E5%29=x%5E%285%2F6%29 ALIGN=MIDDLE  ALT=\"root%286%2Cx%5E5%29=x%5E%285%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But simplification gets tricky. However, since this expression is true\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt[n]{x^m}=x^{\frac{m}{n}}\">\r<BR>\n" );
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document.write( "We'll have an easier way to simplify. So we can let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > become <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^{\frac{1}{2}}\"> and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cx%29 ALIGN=MIDDLE  ALT=\"root%283%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > become <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^{\frac{1}{3}}\">. So we'll get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^{\frac{1}{2}}*x^{\frac{1}{3}}=x^{\frac{1}{2}+\frac{1}{3}}=x^{\frac{5}{6}}\">.  \r<BR>\n" );
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document.write( "This is just one of the many examples where exponent notation is easier to use.\r<BR>\n" );
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