document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201476>Question 1201476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^24=w<BR>\n" );
document.write( "y^40=w<BR>\n" );
document.write( "xyz^12=w\r<BR>\n" );
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document.write( "xyz=/=1<BR>\n" );
document.write( "x,y,z >1\r<BR>\n" );
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document.write( "x=<BR>\n" );
document.write( "y=<BR>\n" );
document.write( "w=<BR>\n" );
document.write( "z= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835861 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835861\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E24=w ALIGN=MIDDLE  ALT=\"x%5E24=w\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=w%5E%281%2F24%29 ALIGN=MIDDLE  ALT=\"x=w%5E%281%2F24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E40=w ALIGN=MIDDLE  ALT=\"y%5E40=w\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=w%5E%281%2F40%29 ALIGN=MIDDLE  ALT=\"y=w%5E%281%2F40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xyz%5E12=w ALIGN=MIDDLE  ALT=\"xyz%5E12=w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%5E%281%2F24%29%29%28w%5E%281%2F40%29%29%28z%5E12%29=w ALIGN=MIDDLE  ALT=\"%28w%5E%281%2F24%29%29%28w%5E%281%2F40%29%29%28z%5E12%29=w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%5E%285%2F120%29%29%28w%5E%283%2F120%29%29%28z%5E12%29=w ALIGN=MIDDLE  ALT=\"%28w%5E%285%2F120%29%29%28w%5E%283%2F120%29%29%28z%5E12%29=w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%5E%288%2F120%29%29%28z%5E12%29=w ALIGN=MIDDLE  ALT=\"%28w%5E%288%2F120%29%29%28z%5E12%29=w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%5E%281%2F15%29%29%28z%5E12%29=w ALIGN=MIDDLE  ALT=\"%28w%5E%281%2F15%29%29%28z%5E12%29=w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E12=w%5E%2814%2F15%29 ALIGN=MIDDLE  ALT=\"z%5E12=w%5E%2814%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=w%5E%2814%2F180%29=w%5E%287%2F90%29 ALIGN=MIDDLE  ALT=\"z=w%5E%2814%2F180%29=w%5E%287%2F90%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The system of equations is indeterminate; there is an infinite family of solutions.<br><BR>\n" );
document.write( "ANSWERS:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=p%5E90%29 ALIGN=MIDDLE  ALT=\"w=p%5E90%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where p is any number (except 1, according to the problem description)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=w%5E%281%2F24%29=p%5E%2890%2F24%29=p%5E%2815%2F4%29 ALIGN=MIDDLE  ALT=\"x=w%5E%281%2F24%29=p%5E%2890%2F24%29=p%5E%2815%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=w%5E%281%2F40%29=p%5E%2890%2F40%29=p%5E%289%2F4%29 ALIGN=MIDDLE  ALT=\"y=w%5E%281%2F40%29=p%5E%2890%2F40%29=p%5E%289%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=w%5E%287%2F90%29 ALIGN=MIDDLE  ALT=\"z=w%5E%287%2F90%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E12=w%5E%2884%2F90%29=p%5E84 ALIGN=MIDDLE  ALT=\"z%5E12=w%5E%2884%2F90%29=p%5E84\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xyz%5E12=%28%28p%5E%2815%2F4%29%29%28p%5E%289%2F4%29%29%28p%5E84%29%29=p%5E90=w ALIGN=MIDDLE  ALT=\"xyz%5E12=%28%28p%5E%2815%2F4%29%29%28p%5E%289%2F4%29%29%28p%5E84%29%29=p%5E90=w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
document.write( "\n" );
document.write( "x^24=w --> x=w^(1/24)<br><BR>\n" );
document.write( "y^40=w --> y=w^(1/40)<br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "xyz^12=w<BR>\n" );
document.write( "(w^(1/24))*(w^(1/40))*(z^12)=w<BR>\n" );
document.write( "(w^(5/120))*(w^(3/120))*(z^12)=w<BR>\n" );
document.write( "(w^(8/120))*(z^12)=w<BR>\n" );
document.write( "(w^(1/15))*(z^12)=w<BR>\n" );
document.write( "z^12=w^(14/15)<BR>\n" );
document.write( "z=w^(14/180)=w^(7/90)<br><BR>\n" );
document.write( "The system of equations is indeterminate; there is an infinite family of solutions.<br><BR>\n" );
document.write( "ANSWERS:<br><BR>\n" );
document.write( "w=p^90 where p is any number (except 1, according to the problem description)<br><BR>\n" );
document.write( "x=w^(1/24)=p^(90/24)=p^(15/4)<BR>\n" );
document.write( "y=w^(1/40)=p^(90/40)=p^(9/4)<BR>\n" );
document.write( "z=w^(7/90)<BR>\n" );
document.write( "z^12=w^(84/90)=p^84<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "xyz^12=((p^(15/4))*(p^(9/4))*(p^84))=(p^6)(p^84)=p^90=w<br>\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );