document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=448057>Question 448057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When rewriting an exponential expression with a negative exponent and positive base to an expression containing only a positive exponent, does the sign of the base change?<BR>\n" );
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document.write( "No; the negative in the exponent means \"invert the base\";<BR>\n" );
document.write( "it does not mean you should change the sign of the base. <BR>\n" );
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document.write( "Ex:<BR>\n" );
document.write( "y = 10*2^(-t)<BR>\n" );
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document.write( "y = 10*(1/2)^t<BR>\n" );
document.write( "QUESTION:  Please explain what you mean when you say invert the base, it does not mean you should change the sign of the base. Im having a hard time explaning this to my classmates.... I would appreciate help with this....Sincere thanks <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 #308442 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=308442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you talk about inversion or inverting, there are 2 basic kinds\r<BR>\n" );
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document.write( "1) Additive Inverse: Take any number and change the sign. For example, inverting 2 gives us -2. Inverting -10 gives us 10.\r<BR>\n" );
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document.write( "2) Multiplicative Inverse: Take any number and reciprocate it. If this is a whole number, divide by 1 and then flip the fraction. Ex: Invert 2 to get <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;\" > (note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=2%2F1 ALIGN=MIDDLE  ALT=\"2=2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >). Ex: Invert <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F1=3 ALIGN=MIDDLE  ALT=\"3%2F1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the inverting you're talking about is the multiplicative kind. Why? Because exponents are a condensed way of writing repeated multiplication. For example <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3=3%2A3%2A3 ALIGN=MIDDLE  ALT=\"3%5E3=3%2A3%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4=3%2A3%2A3%2A3 ALIGN=MIDDLE  ALT=\"3%5E4=3%2A3%2A3%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3 ALIGN=MIDDLE  ALT=\"3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4 ALIGN=MIDDLE  ALT=\"3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E3%29%2F%283%5E4%29=%283%2A3%2A3%29%2F%283%2A3%2A3%2A3%29=1%2F3 ALIGN=MIDDLE  ALT=\"%283%5E3%29%2F%283%5E4%29=%283%2A3%2A3%29%2F%283%2A3%2A3%2A3%29=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E3%29%2F%283%5E4%29=3%5E%283-4%29=3%5E%28-1%29 ALIGN=MIDDLE  ALT=\"%283%5E3%29%2F%283%5E4%29=3%5E%283-4%29=3%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28-1%29=1%2F3 ALIGN=MIDDLE  ALT=\"3%5E%28-1%29=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Another way to look at it: When you go from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3 ALIGN=MIDDLE  ALT=\"3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4 ALIGN=MIDDLE  ALT=\"3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you're multiplying by 3. But to go backwards, you do the opposite of multiplication and you divide by 3, or you multiply by the multiplicative inverse of 3.  </SPAN>\n" );
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