document.write( "Question 387076: Find the units digit for 7^197 without using a calculator. Explain how you found your answer.\r
\n" ); document.write( "\n" ); document.write( "I am completely confused with this!
\n" ); document.write( "I tried doing 7^1 to get 7, then 7^2 but there isnt a pattern.... \n" ); document.write( "
Algebra.Com's Answer #273603 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Find the units digit for 7^197 without using a calculator.
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\n" ); document.write( "Without using a calc you can find that the last digit is repeated every 4 power raises
\n" ); document.write( "7^1 = 7
\n" ); document.write( "7^2 = 9; last digit when you multiply previous last digit 7*7 = 9
\n" ); document.write( "7^3 = 3; last digit when you multiply previous last digit 7*9 = 3
\n" ); document.write( "7^4 = 1; last digit when you multiply previous last digit 7*3 = 1
\n" ); document.write( "7^5 = 7; \" \" \" \" \" \" \" 7*1 = 7
\n" ); document.write( "7^6 = 9; \" \" \" \" \" \" \" 7*7 = 9
\n" ); document.write( "7^7 = 3; \" \" \" \" \" \" \" 7*9 = 3
\n" ); document.write( "7^8 = 1; \" \" \" \" \" \" \" 7*3 = 1
\n" ); document.write( "7^9 = 7; \" \" \" \" \" \" \" 7*1 = 7
\n" ); document.write( "7^10= 9; \" \" \" \" \" \" \" 7*7 = 9
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\n" ); document.write( "Can you see the pattern here? repeats after every 4th power
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\n" ); document.write( "Using long diviion, find the remainder 197/4; that would be 1
\n" ); document.write( "Therefore the last digit should be 7
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