document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164864>Question 164864</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the ones's digit of 8^1007?\r<BR>\n" );
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document.write( "THANK YOU SO MUCH! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121489 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the ones's digit of 8^1007? <BR>\n" );
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document.write( "The one's digit of any even number (except zero) to a power of a multiple of 4, is 6.  That is, 8^(4*n) --> xxxxxxxx6 (n is an integer).<BR>\n" );
document.write( "1007 = 4*251 + 3.<BR>\n" );
document.write( "8^1007 = (8^1004)*(8^3)<BR>\n" );
document.write( "8^3 = 512.<BR>\n" );
document.write( "Multiplying an even number by 6 does not change the one's digit.<BR>\n" );
document.write( "So, the one's digit of 8^1007 is 2.<BR>\n" );
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document.write( "PS  All calculators have a limit on their resolution, and they can only generate results to a certain number of significant figures.  This does not mean that the digits to the right are actually zeroes, but only that the calculator has a limited ability to generate and display a limited number of digits, and it fills in the space with zeroes. </SPAN>\n" );
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