document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=427266>Question 427266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (5th root of 2x^2y)^3<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 #297133 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=297133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'm assuming you want to simplify this as much as possible.\r<BR>\n" );
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document.write( "you are starting off with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%285%2C2x%5E2y%29%29%5E3 ALIGN=MIDDLE  ALT=\"%28root%285%2C2x%5E2y%29%29%5E3\"   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%285%2C2x%5E2y%29 ALIGN=MIDDLE  ALT=\"root%285%2C2x%5E2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2y%29%5E%281%2F5%29 ALIGN=MIDDLE  ALT=\"%282x%5E2y%29%5E%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your expression becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x%5E2y%29%5E%281%2F5%29%29%5E3 ALIGN=MIDDLE  ALT=\"%28%282x%5E2y%29%5E%281%2F5%29%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since, in general, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29 ALIGN=MIDDLE  ALT=\"%28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then your expression becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2y%29%5E%283%2F5%29 ALIGN=MIDDLE  ALT=\"%282x%5E2y%29%5E%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "singe, in general,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Eb%2Ac%5Ed%2Ae%5Ef%29%5Eg+=+a%5E%28b%2Ag%29%2Ac%5E%28d%2Ag%29%2Ae%5E%28f%2Ag%29 ALIGN=MIDDLE  ALT=\"%28a%5Eb%2Ac%5Ed%2Ae%5Ef%29%5Eg+=+a%5E%28b%2Ag%29%2Ac%5E%28d%2Ag%29%2Ae%5E%28f%2Ag%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then your expression becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%283%2F5%29%2A%28x%5E2%29%5E%283%2F5%29%2Ay%5E%283%2F5%29 ALIGN=MIDDLE  ALT=\"2%5E%283%2F5%29%2A%28x%5E2%29%5E%283%2F5%29%2Ay%5E%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this simplifies to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%283%2F5%29%2Ax%5E%286%2F5%29%2Ay%5E%283%2F5%29 ALIGN=MIDDLE  ALT=\"2%5E%283%2F5%29%2Ax%5E%286%2F5%29%2Ay%5E%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if you can't see it because it is cut off, the exponent over the 2 is 3/5, and the exponent over the x is 6/5 and the exponent over the y is 3/5.\r<BR>\n" );
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document.write( "i have confirmed that the original expression and the final expression are equivalent.\r<BR>\n" );
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document.write( "if that's what you were asking about, then this should be your answer.\r<BR>\n" );
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