document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=609668>Question 609668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I have a question.\r<BR>\n" );
document.write( "\n" );
document.write( "(2(cubedroot of a^2)) / (squareroot of 8a) =\r<BR>\n" );
document.write( "\n" );
document.write( "I know that the answer is:\r<BR>\n" );
document.write( "\n" );
document.write( "(fifthroot of (a/8))\r<BR>\n" );
document.write( "\n" );
document.write( "I just don't understand how to get this??\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #383887 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=383887\">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=%282%28root%283%2C+a%5E2%29%29%29%2F%28sqrt%288a%29%29 ALIGN=MIDDLE  ALT=\"%282%28root%283%2C+a%5E2%29%29%29%2F%28sqrt%288a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Keys to this problem are:<ul><li>Understanding that roots/radicals can be replaced with fractional exponents.</li><li>8 is a power of 2.</li></ul>First let's rewrite 8 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;\" > and 2 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E1 ALIGN=MIDDLE  ALT=\"2%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E1%2A%28root%283%2C+a%5E2%29%29%29%2F%28sqrt%282%5E3%2Aa%29%29 ALIGN=MIDDLE  ALT=\"%282%5E1%2A%28root%283%2C+a%5E2%29%29%29%2F%28sqrt%282%5E3%2Aa%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Replacing the radicals with their fractional exponent equivalent:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E1%2A%28a%5E2%29%5E%281%2F3%29%29%2F%282%5E3%2Aa%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%282%5E1%2A%28a%5E2%29%5E%281%2F3%29%29%2F%282%5E3%2Aa%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we use our rules for exponents to simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E1%2Aa%5E%282%2F3%29%29%2F%282%5E3%2Aa%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%282%5E1%2Aa%5E%282%2F3%29%29%2F%282%5E3%2Aa%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >          Rule: Multiply when raising a power to a power<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E1%2Aa%5E%282%2F3%29%29%2F%28%282%5E3%29%5E%281%2F2%29%2Aa%5E%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"%282%5E1%2Aa%5E%282%2F3%29%29%2F%28%282%5E3%29%5E%281%2F2%29%2Aa%5E%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Rule: (a*b)^q = a^q*b*q<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E1%2Aa%5E%282%2F3%29%29%2F%282%5E%283%2F2%29%2Aa%5E%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"%282%5E1%2Aa%5E%282%2F3%29%29%2F%282%5E%283%2F2%29%2Aa%5E%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >       Rule: Power of a power<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%281-%283%2F2%29%29%2Aa%5E%28%282%2F3%29-%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"2%5E%281-%283%2F2%29%29%2Aa%5E%28%282%2F3%29-%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >           Rule: Subtract exp. when dividing<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28-%281%2F2%29%29%2Aa%5E%281%2F6%29 ALIGN=MIDDLE  ALT=\"2%5E%28-%281%2F2%29%29%2Aa%5E%281%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%281%2F6%29%2F2%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"a%5E%281%2F6%29%2F2%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                       Rule: Negative exponents<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%281%2F6%29%2F2%5E%283%2F6%29 ALIGN=MIDDLE  ALT=\"a%5E%281%2F6%29%2F2%5E%283%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Match the denominators in the exponents<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2C+a%29%2Froot%286%2C+2%5E3%29 ALIGN=MIDDLE  ALT=\"root%286%2C+a%29%2Froot%286%2C+2%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rule: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28t%2Fu%29+=+root%28u%2C+a%5Et%29 ALIGN=MIDDLE  ALT=\"a%5E%28t%2Fu%29+=+root%28u%2C+a%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2C+a%29%2Froot%286%2C+8%29 ALIGN=MIDDLE  ALT=\"root%286%2C+a%29%2Froot%286%2C+8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2C+a%2F8%29 ALIGN=MIDDLE  ALT=\"root%286%2C+a%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rule: <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;\" ><BR>\n" );
document.write( "So the answer is the 6th root of a/8, not the 5th root. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );