document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=977126>Question 977126</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following is the greatest?<BR>\n" );
document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E210 ALIGN=MIDDLE  ALT=\"3%5E210\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E140 ALIGN=MIDDLE  ALT=\"7%5E140\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%5E105 ALIGN=MIDDLE  ALT=\"17%5E105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31%5E84 ALIGN=MIDDLE  ALT=\"31%5E84\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "Please give detailed solution.<BR>\n" );
document.write( "(NOTE: Don't use logarithm. It has been removed from syllabus, and I have to make my students understand without using log) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598686 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=598686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "We can eliminate a for the reason Alan gave.\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 7^{140}\ =\ (8\ -\ 1)^{140}\ =\ (2^3\ -\ 1)^{140}\ =\ 2^{420}\ -\ 140\cdot 2^{417}\ +\ ...\">\r<BR>\n" );
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document.write( "By the binomial theorem, and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 17^{105}\ =\ (16\ +\ 1)^{105}\ =\ (2^4\ -\ 1)^{105}\ =\ 2^{420}\ +\ 105\cdot 2^{416}\ +\ ...\">\r<BR>\n" );
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document.write( "Notice that in the expansion of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  (8\ -\ 1)^{140}\">, the signs alternate, but in the expansion of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (16\ +\ 1)^{105}\"> the signs are all positive.  Therefore\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 17^{105}\ >\ 7^{140}\">\r<BR>\n" );
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document.write( "Similarly, the first term of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 31^{84}\ =\ (32\ -\ 1)^{84}\"> will be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2^{420}\"> and the terms will alternate, hence\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 17^{105}\ >\ 31^{84}\">\r<BR>\n" );
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document.write( "Therefore, answer c, as Alan's calculator confirms.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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