document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168709>Question 168709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a). Evaluate 6^,5^0,4^0,3^0,2^0,and 1^0. If you are defining 0^0 what value would you give for 0^0?\r<BR>\n" );
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document.write( "0^0 is inderterminate expression. Based on your observation in in part (a) explain why you think 0^0 is indeterminate.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124358 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=124358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ANY number (except 0) to the zeroth power is ALWAYS 1. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E0=1 ALIGN=MIDDLE  ALT=\"1%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E0=1 ALIGN=MIDDLE  ALT=\"2%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E0=1 ALIGN=MIDDLE  ALT=\"3%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E0=1 ALIGN=MIDDLE  ALT=\"4%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E0=1 ALIGN=MIDDLE  ALT=\"5%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E0=1 ALIGN=MIDDLE  ALT=\"6%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, etc.\r<BR>\n" );
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document.write( "Now why did we exclude zero? It turns out that zero to ANY power (except 0) is 0. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5E1=0 ALIGN=MIDDLE  ALT=\"0%5E1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5E2=0 ALIGN=MIDDLE  ALT=\"0%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5E3=0 ALIGN=MIDDLE  ALT=\"0%5E3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5E3=0 ALIGN=MIDDLE  ALT=\"0%5E3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5E4=0 ALIGN=MIDDLE  ALT=\"0%5E4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5E5=0 ALIGN=MIDDLE  ALT=\"0%5E5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, etc.\r<BR>\n" );
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document.write( "So the question is: what is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5E0 ALIGN=MIDDLE  ALT=\"0%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ??? Is is 1 (since the exponent is 0) or is it 0 (since the base is 0)? Since this contradiction occurs (and a few other reasons), this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5E0 ALIGN=MIDDLE  ALT=\"0%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an indeterminate expression. </SPAN>\n" );
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