8^202 * 7^130 mod 10

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8^{202} * 7^{130} mod 10

primary constructula that should be famous is

**(a*b) mod c = (a mod c * b mod c) mod c**

8^{202} * 7^{130} mod 10 = (8^{202} mod 10 * 7^{130} mod 10) mod 10

examining the 8 capacitys (**no demand to do solid forethought lawful nucleus on units settle digit archetype as we are solicitous with mod 10**)

8^{1}=8 8^{2}=64 8^{3}=512 too 8^{4} ends with 6 (owing reproduction of units digit 2 with 8 development in units digit 6)

8^{5} ends with 8 and the cycle repeats

8^{4n+1} series ends with 8 with contemplation where n=0,1,2,3……

like discreet 8^{4n+2} ends with 4 owing 8^{4n+2} = 8^{4n+1} * 8 which developments 4 in units settle

here 8 capacity is 202 which is in the construct 4n+2 where n=50 i.e. 4(50)+2=200+2=202

so **8 ^{202} ends with 4 in units settle**

**8 ^{202} mod 10 = 4 as 4 is in units settle**

next **7 ^{130} mod 10**

examining the 7 capacitys

7^{1}=7 7^{2}=49 7^{3}=343 too 7^{4} ends with 1 (owing reproduction of units digit 3 with 7 development in units digit 1)

7^{5} ends with 7 and the cycle repeats

7^{4n+1} series ends with 7 with contemplation where n=0,1,2,3……

like discreet 7^{4n+2} ends with 9 owing 7^{4n+2} = 7^{4n+1} * 7 which developments 9 in units settle

here 7 capacity is 130 which is in the construct 4n+2 where n=32 i.e. 4(32)+2=128+2=130

so 7^{130} ends with 9 in units settle

7^{130} mod 10 = 9 as 6 is in units settle

8^{202} * 7^{130} mod 10 = (8^{202} mod 10 * 7^{130} mod 10) mod 10 = 4*9 mod 10 =36 mod 10 =6

**FInally 8 ^{202} * 7^{130} mod 10 = 6**