document.write( "Question 170682: Find the ones digit of 7 raised to the 7th power raised to the 7th power. I multiplied 7, 14 times and I'm not sure that is correct. Thank you. \n" ); document.write( "

Algebra.Com's Answer #126000 by vleith(2983) $\"\"$ $\"About$

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Let's write the equation
\n" ); document.write( " $\"%287%5E7%29%5E7\"$ \r
\n" ); document.write( "\n" ); document.write( "Using the power of powers rule, that yields
\n" ); document.write( " $\"7%5E49\"$ \r
\n" ); document.write( "\n" ); document.write( "Now, 7*7 = 49
\n" ); document.write( "49*7 = 343
\n" ); document.write( "343*7 = 2401
\n" ); document.write( "2401 * 7 = 16807\r
\n" ); document.write( "\n" ); document.write( "Look at the ones digit above. You can see the pattern 7,9,3,1,7...
\n" ); document.write( "So the pattern repeats after each group of 4.
\n" ); document.write( "Thus 7^(4x+1) ends in 7
\n" ); document.write( "7^(4x+2) ends in 9
\n" ); document.write( "7^(4x+3) ends in 3
\n" ); document.write( "7^(4x+4) ends in 1\r
\n" ); document.write( "\n" ); document.write( "49/4 = 12.25 = (4*12) + 1
\n" ); document.write( "That means there are 12 groups of 4, plus one left over. That means you will be left with the ones digit ending in 7 \n" ); document.write( "

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