document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=408332>Question 408332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> cube root (x^2y^4) x cube root (x^4y^10)\r<BR>\n" );
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document.write( "i got : x^2 cube root(y^10) is this correct </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287992 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=287992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please don't use \"x\" for multiplication. Use the word \"times\" or use \"*\" (Shift+8).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+x%5E2y%5E4%29+%2A+root%283%2C+x%5E4y%5E10%29 ALIGN=MIDDLE  ALT=\"root%283%2C+x%5E2y%5E4%29+%2A+root%283%2C+x%5E4y%5E10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Your answer, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Aroot%283%2C+y%5E10%29 ALIGN=MIDDLE  ALT=\"x%5E2%2Aroot%283%2C+y%5E10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is correct so far but it is unfinished. There is more simplifying we can do with the remaining cube root.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E10 ALIGN=MIDDLE  ALT=\"y%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not a perfect cube. (Variables are perfect cubes if their exponents are multiples of 3.) But it does have perfect cube factors. Factoring the  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E10 ALIGN=MIDDLE  ALT=\"y%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > into as many perfect cube factors as possible we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Aroot%283%2C+y%5E3%2Ay%5E3%2Ay%5E3%2Ay%29 ALIGN=MIDDLE  ALT=\"x%5E2%2Aroot%283%2C+y%5E3%2Ay%5E3%2Ay%5E3%2Ay%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can 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%2Aroot%28a%2C+q%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to separate the factors inside the cube root into separate cube roots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Aroot%283%2C+y%5E3%29%2Aroot%283%2C+y%5E3%29%2Aroot%283%2C+y%5E3%29%2Aroot%283%2C+y%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The cube roots of the perfect cubes will simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Ay%2Ay%2Ay%2Aroot%283%2C+y%29 ALIGN=MIDDLE  ALT=\"x%5E2%2Ay%2Ay%2Ay%2Aroot%283%2C+y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Ay%5E3%2Aroot%283%2C+y%29 ALIGN=MIDDLE  ALT=\"x%5E2%2Ay%5E3%2Aroot%283%2C+y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the fully simplified expression. </SPAN>\n" );
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