document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126172>Question 126172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Describe two laws of exponents and provide an example illustrating each law.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92462 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=92462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Exponent Law # 1:\r<BR>\n" );
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document.write( "Let's say you have the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex ALIGN=MIDDLE  ALT=\"2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now, if you want to square this entire expression, you would simply say\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E3%29%5E2 ALIGN=MIDDLE  ALT=\"%282%5E3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To go even further, you can use an exponent law that states: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Ey%29%5Ez=x%5E%28y%2Az%29 ALIGN=MIDDLE  ALT=\"%28x%5Ey%29%5Ez=x%5E%28y%2Az%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, when you have 2 exponents (ie one exponent is raised to another exponent), you simply multiply the two exponents and that product will become the new exponent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E3%29%5E2 ALIGN=MIDDLE  ALT=\"%282%5E3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%283%2A2%29 ALIGN=MIDDLE  ALT=\"2%5E%283%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the previous identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Ey%29%5Ez=x%5E%28y%2Az%29 ALIGN=MIDDLE  ALT=\"%28x%5Ey%29%5Ez=x%5E%28y%2Az%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to rewrite the expression. So we're simply going to multiply the exponents 3 and 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%286%29 ALIGN=MIDDLE  ALT=\"2%5E%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now raise 2 to the 6th power to get 64\r<BR>\n" );
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document.write( "So what we've shown is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E3%29%5E2=64 ALIGN=MIDDLE  ALT=\"%282%5E3%29%5E2=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3=8 ALIGN=MIDDLE  ALT=\"2%5E3=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E3%29%5E2=8%5E2=64 ALIGN=MIDDLE  ALT=\"%282%5E3%29%5E2=8%5E2=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this example illustrates and supports the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Ey%29%5Ez=x%5E%28y%2Az%29 ALIGN=MIDDLE  ALT=\"%28x%5Ey%29%5Ez=x%5E%28y%2Az%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Exponent Law # 2:\r<BR>\n" );
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document.write( "Now let's say you have the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and you want to multiply that by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "One way you could do it is simply note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=x%2Ax ALIGN=MIDDLE  ALT=\"x%5E2=x%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3=x%2Ax%2Ax ALIGN=MIDDLE  ALT=\"x%5E3=x%2Ax%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When you multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Ax%5E3=%28x%2Ax%29%2A%28x%2Ax%2Ax%29=x%2Ax%2Ax%2Ax%2Ax=x%5E5 ALIGN=MIDDLE  ALT=\"x%5E2%2Ax%5E3=%28x%2Ax%29%2A%28x%2Ax%2Ax%29=x%2Ax%2Ax%2Ax%2Ax=x%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "OR\r<BR>\n" );
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document.write( "You can use the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Ey%2Ax%5Ez=x%5E%28y%2Bz%29 ALIGN=MIDDLE  ALT=\"x%5Ey%2Ax%5Ez=x%5E%28y%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This identity basically says that if you multiply two expressions that have the same base, you can simply add the two exponents\r<BR>\n" );
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document.write( "So in our case\r<BR>\n" );
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