Question

The unit's digit for the number 7^76 is____ ?

Answer 1

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