document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126529>Question 126529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Provide the class with a third expression to<BR>\n" );
document.write( "simplify that includes rational (fractional) exponents. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92686 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=92686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say you had the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: the top two exponents from left to right are <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's simplify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%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=%28x%5E%281%2F2%2B3%2F2%29%29%2Fx%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%5E%281%2F2%2B3%2F2%29%29%2Fx%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the numerators by adding the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2Fx%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2Fx%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the exponents <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%2B3%2F2=%281%2B3%29%2F2=4%2F2=2 ALIGN=MIDDLE  ALT=\"1%2F2%2B3%2F2=%281%2B3%29%2F2=4%2F2=2\"   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%5E%282-3%2F4%29 ALIGN=MIDDLE  ALT=\"x%5E%282-3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide the expression by subtracting the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%285%2F4%29 ALIGN=MIDDLE  ALT=\"x%5E%285%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the exponents <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-3%2F4=8%2F4-3%2F4=%288-3%29%2F4=5%2F4 ALIGN=MIDDLE  ALT=\"2-3%2F4=8%2F4-3%2F4=%288-3%29%2F4=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=%28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%285%2F4%29 ALIGN=MIDDLE  ALT=\"x%5E%285%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this says x to the fraction power <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   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=%28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29=x%5E%285%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%5E%281%2F2%29%2Ax%5E%283%2F2%29%29%2Fx%5E%283%2F4%29=x%5E%285%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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