document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=25907>Question 25907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you explain the six laws of exponents with explanations of each one? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13935 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=13935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Em%29%28a%5En%29+=+a%5E%28m%2Bn%29 ALIGN=MIDDLE  ALT=\"%28a%5Em%29%28a%5En%29+=+a%5E%28m%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "eg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3%29%28a%5E2%29+=+a%5E5 ALIGN=MIDDLE  ALT=\"%28a%5E3%29%28a%5E2%29+=+a%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > means (axaxa) x (axa) which is axaxaxaxa --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E5 ALIGN=MIDDLE  ALT=\"a%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Em%29%2F%28a%5En%29+=+a%5E%28m-n%29 ALIGN=MIDDLE  ALT=\"%28a%5Em%29%2F%28a%5En%29+=+a%5E%28m-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "eg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E5%29%28a%5E2%29+=+a%5E3 ALIGN=MIDDLE  ALT=\"%28a%5E5%29%28a%5E2%29+=+a%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > means (axaxaxaxa) divided by (axa) which is axaxa --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3 ALIGN=MIDDLE  ALT=\"a%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Em%29%5En+=+a%5E%28mn%29 ALIGN=MIDDLE  ALT=\"%28a%5Em%29%5En+=+a%5E%28mn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "eg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3%29%5E2+=+a%5E6 ALIGN=MIDDLE  ALT=\"%28a%5E3%29%5E2+=+a%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > means (axaxa) x (axaxa) which is axaxaxaxaxa --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E6 ALIGN=MIDDLE  ALT=\"a%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E0+=+1 ALIGN=MIDDLE  ALT=\"a%5E0+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "eg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3%29%2F%28a%5E3%29+=+1 ALIGN=MIDDLE  ALT=\"%28a%5E3%29%2F%28a%5E3%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > means (axaxa)/(axaxa) which is 1...but the powers in a division subtract, so we get 3-3 which is zero. The zero power of ANY number is 1.\r<BR>\n" );
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document.write( "5. Start with rule 1 and let n be -m. We therefore get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Em%29%28a%5E%28-m%29%29+=+a%5E%28m-m%29 ALIGN=MIDDLE  ALT=\"%28a%5Em%29%28a%5E%28-m%29%29+=+a%5E%28m-m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Em%29%28a%5E%28-m%29%29+=+a%5E0 ALIGN=MIDDLE  ALT=\"%28a%5Em%29%28a%5E%28-m%29%29+=+a%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Em%29%28a%5E%28-m%29%29+=+1 ALIGN=MIDDLE  ALT=\"%28a%5Em%29%28a%5E%28-m%29%29+=+1\"   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%28-m%29+=+1%2F%28a%5Em%29 ALIGN=MIDDLE  ALT=\"a%5E%28-m%29+=+1%2F%28a%5Em%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "eg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28-2%29 ALIGN=MIDDLE  ALT=\"3%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%283%5E2%29 ALIGN=MIDDLE  ALT=\"1%2F%283%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "6. Start with rule 3 and let n be 1/m. We therefore get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Em%29%5E%281%2Fm%29+=+a%5E%28m%2A%281%2Fm%29%29 ALIGN=MIDDLE  ALT=\"%28a%5Em%29%5E%281%2Fm%29+=+a%5E%28m%2A%281%2Fm%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Em%29%5E%281%2Fm%29+=+a%5E1 ALIGN=MIDDLE  ALT=\"%28a%5Em%29%5E%281%2Fm%29+=+a%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Em%29%5E%281%2Fm%29+=+a ALIGN=MIDDLE  ALT=\"%28a%5Em%29%5E%281%2Fm%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, we raise a number \"a\" to power m and then raise to power 1/m and we get the answer \"a\".\r<BR>\n" );
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document.write( "So, the power 1/m means the \"opposite of raising to power m\", ie it is the mth root.\r<BR>\n" );
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document.write( "eg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"25%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the square root of 25.<BR>\n" );
document.write( "eg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%5E%281%2F5%29 ALIGN=MIDDLE  ALT=\"32%5E%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the fifth root of 32.\r<BR>\n" );
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document.write( "jon<BR>\n" );
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