document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=213709>Question 213709</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073206042/algebrahomeworkh>Elementary & Intermediate</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Last digit.  Find the last digit in 3^9999.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161440 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=161440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Last digit. Find the last digit in 3^9999.<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "1st power last digit: 3<BR>\n" );
document.write( "2nd power last digit: 9<BR>\n" );
document.write( "3rd power last digit: 7<BR>\n" );
document.write( "4rh power last digit: 1<BR>\n" );
document.write( "5th power last digit: 3<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "So there is a 5-step cycle<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "9999/5 = 1999  with a remainder of 4<BR>\n" );
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document.write( "So 3^(9999) = 3^(5*1999 + 4)<BR>\n" );
document.write( "= (3^5)^1999 * 3^4<BR>\n" );
document.write( "= 3*3^4<BR>\n" );
document.write( "= 3^5<BR>\n" );
document.write( "= 3<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );