document.write( "Question 783195: what is the ones (or unit) digit in 2^4000 \n" ); document.write( "
Algebra.Com's Answer #476925 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "21 = 2\r\n" ); document.write( "22 = 4\r\n" ); document.write( "23 = 8\r\n" ); document.write( "24 = 16\r\n" ); document.write( "25 = 32\r\n" ); document.write( "26 = 64\r\n" ); document.write( "27 = 128\r\n" ); document.write( "28 = 256\r\n" ); document.write( "29 = 512\r\n" ); document.write( "210 = 1024\r\n" ); document.write( "211 = 2048\r\n" ); document.write( "212 = 4096\r\n" ); document.write( "213 = 8192\r\n" ); document.write( "214 = 16384\r\n" ); document.write( "215 = 32768\r\n" ); document.write( "216 = 65536\r\n" ); document.write( "\r\n" ); document.write( "As you can see the units digits go 2,4,8,6,2,4,8,6,...\r\n" ); document.write( "\r\n" ); document.write( "Every time the exponent to which 2 is raised is a \r\n" ); document.write( "multiple of 4, the units digit is a 6.\r\n" ); document.write( "\r\n" ); document.write( "Therefore since 4000 is a multiple of 4,\r\n" ); document.write( "\r\n" ); document.write( "24000 has units digit 6.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |