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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