document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=395152>Question 395152</A>: <I><SPAN STYLE=\"word-break: break-all;\"> why is the answer to<BR>\n" );
document.write( "cube root of 9 times cubed root of 6 <BR>\n" );
document.write( "DIVIDED BY<BR>\n" );
document.write( "6 root 2 times 6 root 2<BR>\n" );
document.write( "= 3? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280542 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=280542\">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=%28root%283%2C+9%29%2Aroot%283%2C+6%29%29%2F%28root%286%2C+2%29%2Aroot%286%2C+2%29%29 ALIGN=MIDDLE  ALT=\"%28root%283%2C+9%29%2Aroot%283%2C+6%29%29%2F%28root%286%2C+2%29%2Aroot%286%2C+2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First we can use a property of radicals, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to multiply in both the numerator and the denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+9%2A6%29%2Froot%286%2C+2%2A2%29 ALIGN=MIDDLE  ALT=\"root%283%2C+9%2A6%29%2Froot%286%2C+2%2A2%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=root%283%2C+54%29%2Froot%286%2C+2%5E2%29 ALIGN=MIDDLE  ALT=\"root%283%2C+54%29%2Froot%286%2C+2%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I left the radicand in the denominator in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2 ALIGN=MIDDLE  ALT=\"2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for reasons that will become clear soon.<BR>\n" );
document.write( "Next we use fractional exponents in the denominator to help us simplify further. Using the pattern <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%5Eb%29+=+a%5E%28b%2Fa%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%5Eb%29+=+a%5E%28b%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can rewrite the denominator as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%282%2F6%29 ALIGN=MIDDLE  ALT=\"2%5E%282%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can see that this fraction will reduce to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"2%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Writing this back in radical form we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+2%5E1%29 ALIGN=MIDDLE  ALT=\"root%283%2C+2%5E1%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=root%283%2C+2%29 ALIGN=MIDDLE  ALT=\"root%283%2C+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now our fraction looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+54%29%2Froot%283%2C+2%29 ALIGN=MIDDLE  ALT=\"root%283%2C+54%29%2Froot%283%2C+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can use another property of radicals, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%29%2Froot%28a%2C+q%29++=+root%28a%2C+p%2Fq%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%29%2Froot%28a%2C+q%29++=+root%28a%2C+p%2Fq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to combine the two radicals into one:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+54%2F2%29 ALIGN=MIDDLE  ALT=\"root%283%2C+54%2F2%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=root%283%2C+27%29 ALIGN=MIDDLE  ALT=\"root%283%2C+27%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3+=+27 ALIGN=MIDDLE  ALT=\"3%5E3+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this cube root becomes a 3! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );