document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250287>Question 250287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Describe two laws of exponents and provide an example illustrating each law. Explain how to simplify your expression. How do the laws work with rational exponents? Provide a expression to simplify that includes rational (fractional) exponents. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185404 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185404\">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=%28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29 ALIGN=MIDDLE  ALT=\"%28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E4%29%5E2+=+2%5E%284%2A2%29+=+2%5E8+=+256 ALIGN=MIDDLE  ALT=\"%282%5E4%29%5E2+=+2%5E%284%2A2%29+=+2%5E8+=+256\"   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=2%5E4+=+2%2A2%2A2%2A2 ALIGN=MIDDLE  ALT=\"2%5E4+=+2%2A2%2A2%2A2\"   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=%282%2A2%2A2%2A2%29%5E2+=+%282%2A2%2A2%2A2%29+%2A+%282%2A2%2A2%2A2%29+=+2%2A2%2A2%2A2%2A2%2A2%2A2%2A2+=+2%5E8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "---------------------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28b%2Fc%29+=+%28a%5Eb%29%5E%281%2Fc%29+=+a%5E%28b%2A%281%2Fc%29%29 ALIGN=MIDDLE  ALT=\"a%5E%28b%2Fc%29+=+%28a%5Eb%29%5E%281%2Fc%29+=+a%5E%28b%2A%281%2Fc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the fractional exponents from left to right are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fc ALIGN=MIDDLE  ALT=\"b%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fc ALIGN=MIDDLE  ALT=\"1%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fc ALIGN=MIDDLE  ALT=\"1%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "this can also be expressed as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28b%2Fc%29+=+%28a%5E%281%2Fc%29%29%5Eb+=+a%5E%28%281%2Fc%29%2Ab%29 ALIGN=MIDDLE  ALT=\"a%5E%28b%2Fc%29+=+%28a%5E%281%2Fc%29%29%5Eb+=+a%5E%28%281%2Fc%29%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28b%2A%281%2Fc%29%29 ALIGN=MIDDLE  ALT=\"a%5E%28b%2A%281%2Fc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the fractional exponents from left to right are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fc ALIGN=MIDDLE  ALT=\"b%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fc ALIGN=MIDDLE  ALT=\"1%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fc ALIGN=MIDDLE  ALT=\"1%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fc ALIGN=MIDDLE  ALT=\"1%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%284%2F2%29+=+%282%5E4%29%5E%281%2F2%29+=+%282%5E%281%2F2%29%29%5E4+=+2%5E%28%281%2F2%29%2A4%29+=+2%5E2+=+4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the fractional exponents from left to right are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F2 ALIGN=MIDDLE  ALT=\"4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   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=2%5E4+=+16 ALIGN=MIDDLE  ALT=\"2%5E4+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E%281%2F2%29+=+root%282%2C16%29+=+4 ALIGN=MIDDLE  ALT=\"16%5E%281%2F2%29+=+root%282%2C16%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the fractional exponent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   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=2%5E%281%2F2%29+=+root%282%2C2%29 ALIGN=MIDDLE  ALT=\"2%5E%281%2F2%29+=+root%282%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%282%2C2%29%29%5E4+=+4 ALIGN=MIDDLE  ALT=\"%28root%282%2C2%29%29%5E4+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the fractional exponent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   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=a%5E%281%2Fc%29+=+root%28c%2Ca%29 ALIGN=MIDDLE  ALT=\"a%5E%281%2Fc%29+=+root%28c%2Ca%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "the fractional exponent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fc ALIGN=MIDDLE  ALT=\"1%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E%281%2F2%29+=+root%282%2C16%29+=+4 ALIGN=MIDDLE  ALT=\"16%5E%281%2F2%29+=+root%282%2C16%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "the fractional exponent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28b%2Fc%29+=+%28root%28c%2Ca%29%29%5Eb+=+root%28c%2Ca%5Eb%29 ALIGN=MIDDLE  ALT=\"a%5E%28b%2Fc%29+=+%28root%28c%2Ca%29%29%5Eb+=+root%28c%2Ca%5Eb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "the fractional exponent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fc ALIGN=MIDDLE  ALT=\"b%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%284%2F2%29+=+%28root%282%2C2%29%29%5E4+=+root%282%2C2%5E4%29 ALIGN=MIDDLE  ALT=\"2%5E%284%2F2%29+=+%28root%282%2C2%29%29%5E4+=+root%282%2C2%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4. \r<BR>\n" );
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document.write( "the fractional exponent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F2%29 ALIGN=MIDDLE  ALT=\"%284%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "you can take <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;\" > first and then apply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E%281%2F2%29+=+4 ALIGN=MIDDLE  ALT=\"16%5E%281%2F2%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "the fractional exponent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   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 take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%281%2F2%29+=+sqrt%282%2C2%29 ALIGN=MIDDLE  ALT=\"2%5E%281%2F2%29+=+sqrt%282%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > first and then apply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2C2%29%5E4+=+4 ALIGN=MIDDLE  ALT=\"sqrt%282%2C2%29%5E4+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "the fractional exponent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "either way you get the same answer (4). </SPAN>\n" );
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