Posted by Jeff on Thursday, January 17, 2013 at 3:40am.
The unit's digit for the number 7^76 is____ ?

MATH  Reiny, Thursday, January 17, 2013 at 10:05am
look at powers of 7
7^0 ends in 1
7^1 ends in 7
7^2 ends in 9
7^3 ends in 3
7^4 ends in 1
7^5 ends in 7
7^6 ends in 9
etc.
So it repeats after 4 digits
If we divide the exponent by 4, all we have to do is look at the remainder, and match it with the exponents of the above chart.
eg. for 7^10 (your calculator can still do that one)
it ends in????
10÷4 leaves a remainder of 2 and from the above, for an exponent of 2 our number should end in 9
10^7 ends in a 9 !!!
So...
for 7^76 , dividing 76 by 4 leaves a remainder of 0
so 7^76 end in 1
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