document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037010>Question 1037010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rewrite without rational exponents and simplify if possible\r<BR>\n" );
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document.write( "(5a^2b)^3/5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #651767 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=651767\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i translate this to read:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Aa%5E2%2Ab%29%5E%283%2F5%29 ALIGN=MIDDLE  ALT=\"%285%2Aa%5E2%2Ab%29%5E%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this is equivalent to<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%285%2Aa%5E2%2Ab%29%5E3%29%5E%281%2F5%29 ALIGN=MIDDLE  ALT=\"%28%285%2Aa%5E2%2Ab%29%5E3%29%5E%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%5E3%2A%28a%5E2%29%5E3%2Ab%5E3%29%5E%281%2F5%29 ALIGN=MIDDLE  ALT=\"%285%5E3%2A%28a%5E2%29%5E3%2Ab%5E3%29%5E%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28125%2Aa%5E6%2Ab%5E3%29%5E%281%2F5%29 ALIGN=MIDDLE  ALT=\"%28125%2Aa%5E6%2Ab%5E3%29%5E%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equivalent to the fifth root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28125%2Aa%5E6%2Ab%5E3%29 ALIGN=MIDDLE  ALT=\"%28125%2Aa%5E6%2Ab%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "i confirmed by assigning the value of 7 to a and the value of 9 to b and evaluated the original expression and the final expression.\r<BR>\n" );
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document.write( "i got the original expression = 101.4016814<BR>\n" );
document.write( "i got the final expression = 101.4016814\r<BR>\n" );
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document.write( "since the values are the same, i assumed that the solution is correct.\r<BR>\n" );
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document.write( "the basic concepts used are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Eb%29%5Ec ALIGN=MIDDLE  ALT=\"%28a%5Eb%29%5Ec\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28b%2Ac%29 ALIGN=MIDDLE  ALT=\"a%5E%28b%2Ac%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=x%5E%28a%2Fb%29 ALIGN=MIDDLE  ALT=\"x%5E%28a%2Fb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Ea%29%5E%281%2Fb%29 ALIGN=MIDDLE  ALT=\"%28x%5Ea%29%5E%281%2Fb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the b root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Ea%29 ALIGN=MIDDLE  ALT=\"%28x%5Ea%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E2%29%5E3 ALIGN=MIDDLE  ALT=\"%282%5E2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%282%2A3%29 ALIGN=MIDDLE  ALT=\"2%5E%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E6 ALIGN=MIDDLE  ALT=\"2%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 64.\r<BR>\n" );
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document.write( "since 2^2 = 4 and 4^3 = 64, this confirms the concept is correct.\r<BR>\n" );
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document.write( "also:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%284%2F2%29 ALIGN=MIDDLE  ALT=\"2%5E%284%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E4%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%282%5E4%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E4%29 ALIGN=MIDDLE  ALT=\"%282%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.\r<BR>\n" );
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document.write( "since 2^4 = 16 and the square root of 16 is equal to 4, this confirms the concept is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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