document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=373073>Question 373073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> cube root of 128x^5y^4z^3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #265906 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=265906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+128x%5E5y%5E4z%5E3%29 ALIGN=MIDDLE  ALT=\"root%283%2C+128x%5E5y%5E4z%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To simplify a cube root, look for perfect cube factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+64%2A2%2Ax%5E3%2Ax%5E2%2Ay%5E3%2Ay%2Az%5E3%29 ALIGN=MIDDLE  ALT=\"root%283%2C+64%2A2%2Ax%5E3%2Ax%5E2%2Ay%5E3%2Ay%2Az%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then we use a property of radicals, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29+%2A+root%28a%2C+q%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29+%2A+root%28a%2C+q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to separate the perfect cube factors into their own cube roots. (We will just leave all the factors which are not perfect cubes in a single cube root.):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+64%29%2Aroot%283%2C+x%5E3%29%2Aroot%283%2C+y%5E3%29%2Aroot%283%2C+z%5E3%29%2Aroot%283%2C+2%2Ax%5E2%2Ay%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The cube roots of each of the perfect cubes can be simplified:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%2Ay%2Az%2Aroot%283%2C+2x%5E2y%29 ALIGN=MIDDLE  ALT=\"4%2Ax%2Ay%2Az%2Aroot%283%2C+2x%5E2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4xyz%2Aroot%283%2C+2x%5E2y%29 ALIGN=MIDDLE  ALT=\"4xyz%2Aroot%283%2C+2x%5E2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the simplified version of your original expression. </SPAN>\n" );
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