document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112648>Question 112648</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0669383171/algebrahomeworkh>Algebra 2 An Integrated Approach</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How do you multiply two eponential powers to the 4th root, sush as: 3 to the 4th root x 729 to the 4th root?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82122 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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/cgi-bin/show-face.mpl?user=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the multiplication rule for radicals:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28a%29%2Asqrt%28b%29+=+sqrt%28ab%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28a%29%2Asqrt%28b%29+=+sqrt%28ab%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > provided a and b are not both negative numbers!\r<BR>\n" );
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document.write( "Likewise <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28n%2Ca%29%2Aroot%28n%2Cb%29+=+root%28n%2Cab%29+ ALIGN=MIDDLE  ALT=\"root%28n%2Ca%29%2Aroot%28n%2Cb%29+=+root%28n%2Cab%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In your specific case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2Ca%29%2Aroot%284%2Cb%29+=+root%284%2Cab%29+ ALIGN=MIDDLE  ALT=\"root%284%2Ca%29%2Aroot%284%2Cb%29+=+root%284%2Cab%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Meanwhile, since you are doing a fourth root, be looking for perfect 4th powers that may be factors of these numbers.  In particular, look for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4=16 ALIGN=MIDDLE  ALT=\"2%5E4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4=+81 ALIGN=MIDDLE  ALT=\"3%5E4=+81\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  In this case, notice that 729 is divisible by 81, and can be written 729 = 81*9.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C3%29%2Aroot%284%2C729%29+ ALIGN=MIDDLE  ALT=\"root%284%2C3%29%2Aroot%284%2C729%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%284%2C3%29%2Aroot%284%2C81%29%2Aroot%284%2C9%29+ ALIGN=MIDDLE  ALT=\"+root%284%2C3%29%2Aroot%284%2C81%29%2Aroot%284%2C9%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%284%2C3%29+%2A3%2A+root%284%2C9%29 ALIGN=MIDDLE  ALT=\"root%284%2C3%29+%2A3%2A+root%284%2C9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Aroot%284%2C3%29%2Aroot%284%2C9%29+ ALIGN=MIDDLE  ALT=\"3%2Aroot%284%2C3%29%2Aroot%284%2C9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Aroot%284%2C27%29+ ALIGN=MIDDLE  ALT=\"3%2Aroot%284%2C27%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For additional explanation on roots, please see my Lesson Plan in algebra.com.  Or even better, go to my own website by clicking on my tutor name \"rapaljer\" anywhere in algebra.com.  Click on my first link, which is \"Basic or Intermediate Algebra: One Step at a Time\", and look in Chapter 5 for Section 5.02 \"Cube Roots and More\".  Also see my MATH IN LIVING COLOR PAGES.  Look for Basic Algebra Chapter 5 or for more advanced problems see Intermediate Algebra Chapter 3.  I think you will find this website helpful.  \r<BR>\n" );
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document.write( "R^2 <BR>\n" );
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