document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72588>Question 72588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (125/8X to the 12 power ) all that raised to a -2/3 power. So 125 over 8X to the 12th power and all of that raised to the -2/3 power<BR>\n" );
document.write( "I tried 125 to the -2/3 over 8 to the -2/3 (times) 8X to the -8 and got 125 over 8X to the -8.then fliped it because it is a negative exponent which would be 8X to the 8th over 125 which reduces to 2X to the 8th over 5? I really don't understand this at all. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51907 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=51907\">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=%28%28125%2F%288%2AX%29%29%5E12%29%5E%28-2%2F3%29 ALIGN=MIDDLE  ALT=\"%28%28125%2F%288%2AX%29%29%5E12%29%5E%28-2%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Sort of a complex problem.  What can be done for openers is to recall that when you raise<BR>\n" );
document.write( "a power to a power, you can just multiply the two exponents.  So you can simplify the problem<BR>\n" );
document.write( "by multiplying the (-2/3) exponent times the (+12) exponent to get a new single exponent of (-8).<BR>\n" );
document.write( "The problem then becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28125%2F%288%2AX%29%29%5E%28-8%29%29 ALIGN=MIDDLE  ALT=\"%28%28125%2F%288%2AX%29%29%5E%28-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next, to get rid of the negative exponent you can put the term with a positive exponent as<BR>\n" );
document.write( "the denominator of a fraction whose numerator is 1.  The problem then becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%28125%29%2F%288%2AX%29%29%5E8%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28125%29%2F%288%2AX%29%29%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then by exponent rules the terms under the numerator can both be raised to the 8th power to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%28125%5E8%29%2F%28%288%2AX%29%5E8%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28125%5E8%29%2F%28%288%2AX%29%5E8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next multiply the numerator and denominator of this fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%288%2AX%29%5E8%2F%288%2AX%29%5E8%29 ALIGN=MIDDLE  ALT=\"%28%288%2AX%29%5E8%2F%288%2AX%29%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The top<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2AX%29%5E8 ALIGN=MIDDLE  ALT=\"%288%2AX%29%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiplies the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the bottom <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2AX%29%5E8 ALIGN=MIDDLE  ALT=\"%288%2AX%29%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiplies the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28125%5E8%29%2F%28%288%2AX%29%5E8%29%29 ALIGN=MIDDLE  ALT=\"%28%28125%5E8%29%2F%28%288%2AX%29%5E8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "This results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2AX%29%5E8%2F%28%28%28125%5E8%29%2F%28%288%2AX%29%5E8%29%29%2A%288%2AX%29%5E8%29 ALIGN=MIDDLE  ALT=\"%288%2AX%29%5E8%2F%28%28%28125%5E8%29%2F%28%288%2AX%29%5E8%29%29%2A%288%2AX%29%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice the cancellation in the bottom:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2AX%29%5E8%2F%28%28%28125%5E8%29%2Fcross%28%288%2AX%29%5E8%29%29%2Across%288%2AX%29%5E8%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So at this point we are at:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2AX%29%5E8%2F%28125%29%5E8 ALIGN=MIDDLE  ALT=\"%288%2AX%29%5E8%2F%28125%29%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But by the rules of exponents the numerator can be expanded and the problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%5E8%29%2A%28X%5E8%29%2F%28125%5E8%29 ALIGN=MIDDLE  ALT=\"%288%5E8%29%2A%28X%5E8%29%2F%28125%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now, depending on how much further you want to go, you can divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E8 ALIGN=MIDDLE  ALT=\"8%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5E8 ALIGN=MIDDLE  ALT=\"125%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and get (rounded off):<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0000000003%2AX%5E8 ALIGN=MIDDLE  ALT=\"0.0000000003%2AX%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "But maybe you could quit earlier than that or could use scientific notation to get<BR>\n" );
document.write( "an answer of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282.814749767+%2A+10%5E%28-10%29%29%2AX%5E8 ALIGN=MIDDLE  ALT=\"%282.814749767+%2A+10%5E%28-10%29%29%2AX%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you understand exponents a little more.  A lot of practice with various rules<BR>\n" );
document.write( "in doing this problem. </SPAN>\n" );
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