document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=310502>Question 310502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify:\r<BR>\n" );
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document.write( "(27B^1/3C^3/4 ) ^4/3\r\n" );
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document.write( "( 8B^-2/3C^1/2)\r\n" );
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document.write( "Entire expression is in parenthesis with outer exponent 4/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #222003 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=222003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We're going to use the following identities \r<BR>\n" );
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document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%28y%29%29%2F%28x%5E%28z%29%29=x%5E%28y-z%29 ALIGN=MIDDLE  ALT=\"%28x%5E%28y%29%29%2F%28x%5E%28z%29%29=x%5E%28y-z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%28y%29%29%5Ez=x%5E%28y%2Az%29 ALIGN=MIDDLE  ALT=\"%28x%5E%28y%29%29%5Ez=x%5E%28y%2Az%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Fb%29%5Ex=%28a%5Ex%29%2F%28b%5Ex%29 ALIGN=MIDDLE  ALT=\"%28a%2Fb%29%5Ex=%28a%5Ex%29%2F%28b%5Ex%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=%28%2827b%5E%281%2F3%29c%5E%283%2F4%29%5E%22%22%29%2F%288b%5E%28-2%2F3%29c%5E%281%2F2%29%5E%22%22%29%29%5E%284%2F3%29%5E%22%22 ALIGN=MIDDLE   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=%28%2827b%5E%281%2F3-%28-2%2F3%29%29c%5E%283%2F4-1%2F2%29%5E%22%22%29%2F8%29%5E%284%2F3%29%5E%22%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Use identity # 1 to divide the variable terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2827b%5E%281%2F3%2B2%2F3%29c%5E%283%2F4-1%2F2%29%5E%22%22%29%2F8%29%5E%284%2F3%29%5E%22%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3-%28-2%2F3%29 ALIGN=MIDDLE  ALT=\"1%2F3-%28-2%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3%2B2%2F3 ALIGN=MIDDLE  ALT=\"1%2F3%2B2%2F3\"   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=%28%2827b%5E%281%2F3%2B2%2F3%29c%5E%283%2F4-2%2F4%29%5E%22%22%29%2F8%29%5E%284%2F3%29%5E%22%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <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;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F2 ALIGN=MIDDLE  ALT=\"2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F4 ALIGN=MIDDLE  ALT=\"2%2F4\"   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=%28%2827b%5E%28%281%2B2%29%2F3%29c%5E%28%283-2%29%2F4%29%5E%22%22%29%2F8%29%5E%284%2F3%29%5E%22%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions by combining the numerators over the common denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2827b%5E%283%2F3%29c%5E%281%2F4%29%5E%22%22%29%2F8%29%5E%284%2F3%29%5E%22%22 ALIGN=MIDDLE  ALT=\"%28%2827b%5E%283%2F3%29c%5E%281%2F4%29%5E%22%22%29%2F8%29%5E%284%2F3%29%5E%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%2F8%29%5E%284%2F3%29%5E%22%22 ALIGN=MIDDLE  ALT=\"%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%2F8%29%5E%284%2F3%29%5E%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%288%5E%284%2F3%29%5E%22%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Now use identity # 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%28%282%5E3%29%5E%284%2F3%29%5E%22%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3 ALIGN=MIDDLE  ALT=\"2%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=%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%28%282%5E%283%284%2F3%29%29%5E%22%22%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Use identity # 2 to multiply the exponents.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%28%282%5E%2812%2F3%29%5E%22%22%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 3 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F3 ALIGN=MIDDLE  ALT=\"12%2F3\"   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=%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%282%5E4%29 ALIGN=MIDDLE  ALT=\"%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%282%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"%28%2827b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4 ALIGN=MIDDLE  ALT=\"2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 16\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%5E3b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"%28%283%5E3b%5E1c%5E%281%2F4%29%5E%22%22%29%5E%284%2F3%29%5E%22%22%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 27 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3 ALIGN=MIDDLE  ALT=\"3%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=%283%5E%283%284%2F3%29%29b%5E%281%284%2F3%29%29c%5E%28%281%2F4%29%284%2F3%29%29%5E%22%22%29%2F%2816%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Use identity # 2 to multiply the exponents.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E%2812%2F3%29b%5E%284%2F3%29c%5E%284%2F12%29%5E%22%22%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"%283%5E%2812%2F3%29b%5E%284%2F3%29c%5E%284%2F12%29%5E%22%22%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 3 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F3 ALIGN=MIDDLE  ALT=\"12%2F3\"   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=%283%5E4b%5E%284%2F3%29c%5E%281%2F3%29%5E%22%22%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"%283%5E4b%5E%284%2F3%29c%5E%281%2F3%29%5E%22%22%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2881b%5E%284%2F3%29c%5E%281%2F3%29%5E%22%22%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"%2881b%5E%284%2F3%29c%5E%281%2F3%29%5E%22%22%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 3 to the 4th power to get 81\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2827b%5E%281%2F3%29c%5E%283%2F4%29%5E%22%22%29%2F%288b%5E%28-2%2F3%29c%5E%281%2F2%29%5E%22%22%29%29%5E%284%2F3%29%5E%22%22=%2881b%5E%284%2F3%29c%5E%281%2F3%29%5E%22%22%29%2F%2816%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive. </SPAN>\n" );
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