document.write( "Question 657007: what is the unit digit of 2^19? please give a detailed explanation because i still dont get after trying for an hour, thanks. \n" ); document.write( "
Algebra.Com's Answer #409777 by ankor@dixie-net.com(22740)\"\" \"About 
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what is the unit digit of 2^19?
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\n" ); document.write( "A pattern can be demonstrated here
\n" ); document.write( "2^1 = 2
\n" ); document.write( "2^2 = 4
\n" ); document.write( "2^3 = 8
\n" ); document.write( "2^4 = 16
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\n" ); document.write( "2^5 = 32
\n" ); document.write( "2^6 = 64
\n" ); document.write( "2^7 = 128
\n" ); document.write( "2^8 = 256
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\n" ); document.write( "You notice the units are a repeating series, 2,4,8,6 and this will repeat no
\n" ); document.write( "matter how high the exponents go
\n" ); document.write( "So we can say that every exponent that is a multiple of 4 will have unit of 6
\n" ); document.write( "Then the 2,4,8,6 series begins again
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\n" ); document.write( "In our problem, 2^19, we know 2^16 has a unit of 6, start series from there
\n" ); document.write( "2,4,8, 2^19 has a unit of 8, right?
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\n" ); document.write( "Another words
\n" ); document.write( "2^20, 20 is a multiple of 4, so it will have a unit of 6, therefore going back
\n" ); document.write( "one in the series to 2^19, it would be 8, right
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\n" ); document.write( "YOu can find the unit value of any exponent of 2 this way. \r
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