document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314459>Question 314459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2832%5E-1%5E4%29%5E-4%5E5+ ALIGN=MIDDLE  ALT=\"+%2832%5E-1%5E4%29%5E-4%5E5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the exponents are supposed to be negative fractions ^-1/4 and ^-4/5 <BR>\n" );
document.write( "please help :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224834 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=224834\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If I understand you correctly, your expression should look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832%5E%28-1%2F4%29%29%5E%28-4%2F5%29 ALIGN=MIDDLE  ALT=\"%2832%5E%28-1%2F4%29%29%5E%28-4%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Because these is a cropping problem with the formula generator when fractional exponents are used, I will make decimal equivalents to allow you to see what's happening better.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to .25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to .8\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=%2832%5E%28-.25%29%29%5E%28-.8%29 ALIGN=MIDDLE  ALT=\"%2832%5E%28-.25%29%29%5E%28-.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To solve this problem,  you will use two of the rules of exponentiation.\r<BR>\n" );
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document.write( "The first rule is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-n%29+=+1%2Fx%5En ALIGN=MIDDLE  ALT=\"x%5E%28-n%29+=+1%2Fx%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The second rule is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Em%2Fy%5En%29%5Ek+=+x%5E%28m%2Ak%29%2Fy%5E%28n%2Ak%29 ALIGN=MIDDLE  ALT=\"%28x%5Em%2Fy%5En%29%5Ek+=+x%5E%28m%2Ak%29%2Fy%5E%28n%2Ak%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When you have nested parentheses, you always resolve the inner parentheses before resolving the outer parentheses.\r<BR>\n" );
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document.write( "We will follow that rule.\r<BR>\n" );
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document.write( "Your expression to be simplified is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832%5E%28-.25%29%29%5E%28-.8%29 ALIGN=MIDDLE  ALT=\"%2832%5E%28-.25%29%29%5E%28-.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the first rule to resolve the inner parentheses, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F32%5E.25%29%5E%28-.8%29 ALIGN=MIDDLE  ALT=\"%281%2F32%5E.25%29%5E%28-.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the first rule again to resolve the remaining expression, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%281%2F32%5E.25%29%5E%28.8%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%281%2F32%5E.25%29%5E%28.8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the second rule, our expression becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%281%5E%28.8%29%2F32%5E%28.25%2A.8%29%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%281%5E%28.8%29%2F32%5E%28.25%2A.8%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This simplifies further to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%281%5E%28.8%29%2F32%5E%28.2%29%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%281%5E%28.8%29%2F32%5E%28.2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E.8+=+1 ALIGN=MIDDLE  ALT=\"1%5E.8+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%5E%28.2%29+=+2 ALIGN=MIDDLE  ALT=\"32%5E%28.2%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then our expression becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"1%2F%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Our expression resolves to 2.\r<BR>\n" );
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document.write( "You can confirm this answer is correct by plugging the original expression into your calculator and then plugging the final expression into your calculator to see that you get the same answer.\r<BR>\n" );
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document.write( "Use the decimal equivalents of the fractional exponents since they are easier to work with, although you should know how to handle the fractions as well.\r<BR>\n" );
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document.write( "Your original expression with the decimal equivalents of the fractional exponents is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832%5E%28-.25%29%29%5E%28-.8%29 ALIGN=MIDDLE  ALT=\"%2832%5E%28-.25%29%29%5E%28-.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which resolves to 2.\r<BR>\n" );
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document.write( "Your final expression with the decimal equivalents of the fractional exponents is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%281%5E%28.8%29%2F32%5E%28.2%29%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%281%5E%28.8%29%2F32%5E%28.2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which resolves to 2.\r<BR>\n" );
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document.write( "Both expressions resolve to 2 which indicates that the simplification process worked as expected.\r<BR>\n" );
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document.write( "If I were to do this by hand, the progression would look like this:\r<BR>\n" );
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