document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167645>Question 167645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I keep confusing myself with this problem. worksheet states please simplify each of the following. <BR>\n" );
document.write( "sqrt(3x^6)* sqrt(27x^13)= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123538 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=123538\">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=sqrt%283x%5E6%29%2A+sqrt%2827x%5E13%29=sqrt%28%283x%5E6%29%2827x%5E13%29%29=sqrt%28%283%2A27%29%28x%5E6%2Ax%5E13%29%29=sqrt%2881x%5E%2819%29%29=sqrt%2881%29%2Asqrt%28x%5E19%29=9x%5E9%2Asqrt%28x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%5E6%29%2A+sqrt%2827x%5E13%29=9x%5E9%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%283x%5E6%29%2A+sqrt%2827x%5E13%29=9x%5E9%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here are some side notes\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1) All variables are positive so this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2) To multiply variables with exponents (the same variables) simply add the exponents <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6%2Ax%5E13=x%5E%286%2B13%29=x%5E19 ALIGN=MIDDLE  ALT=\"x%5E6%2Ax%5E13=x%5E%286%2B13%29=x%5E19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3) The goal to simplify this is to break 19 into 18+1 where 18 is a multiple of 2 (that way, we can take the square root)\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E19%29=sqrt%28x%5E%2818%2B1%29%29=sqrt%28x%5E18%2Ax%5E1%29=sqrt%28%28x%5E9%29%5E2%2Ax%29=sqrt%28%28x%5E9%29%5E2%29%2Asqrt%28x%29=x%5E9%2Asqrt%28x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );