document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114176>Question 114176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify. (a^3)^6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83175 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=83175\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For this problem, the power rule of exponents applies. That rule states that when you raise<BR>\n" );
document.write( "a quantity that has an exponent to a power, you multiply the exponents and use this product<BR>\n" );
document.write( "as the exponent of the base. For example:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5Ex%29%5Ey+=+b%5E%28x%2Ay%29 ALIGN=MIDDLE  ALT=\"%28b%5Ex%29%5Ey+=+b%5E%28x%2Ay%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Applying this rule to your problem you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3%29%5E6+=+a%5E%283%2A6%29+=+a%5E18 ALIGN=MIDDLE  ALT=\"%28a%5E3%29%5E6+=+a%5E%283%2A6%29+=+a%5E18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the answer you are looking for is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3%29%5E6+=+a%5E18 ALIGN=MIDDLE  ALT=\"%28a%5E3%29%5E6+=+a%5E18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you can also look at it this way:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+=+%28a%2Aa%2Aa%29 ALIGN=MIDDLE  ALT=\"a%5E3+=+%28a%2Aa%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by definition. If you raise <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;\" > to the 6th power you multiply it<BR>\n" );
document.write( "by itself 6 times. That is you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3%29%5E6+=+%28a%5E3%29%2A%28a%5E3%29%2A%28a%5E3%29%2A%28a%5E3%29%2A%28a%5E3%29%2A%28a%5E3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "but then on the right side you can replace each <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;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Aa%2Aa ALIGN=MIDDLE  ALT=\"a%2Aa%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" > and when you<BR>\n" );
document.write( "do that the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3%29%5E6+=+%28a%2Aa%2Aa%29%2A%28a%2Aa%2Aa%29%2A%28a%2Aa%2Aa%29%2A%28a%2Aa%2Aa%29%2A%28a%2Aa%2Aa%29%2A%28a%2Aa%2Aa%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and when you count all the a's on the right side you get 18 of them, all multiplied<BR>\n" );
document.write( "together. This means that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3%29%5E6+=+a%5E18 ALIGN=MIDDLE  ALT=\"%28a%5E3%29%5E6+=+a%5E18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which is the same answer that we got when we multiplied the exponent 3 times the exponent 6<BR>\n" );
document.write( "to get the resulting exponent of 18.<BR>\n" );
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document.write( "Hope this helps you to see what is going on with this problem.<BR>\n" );
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