Question

answer this question with explaination

Answer 1

see the trend of unit place digit:

7^1 =7

7^2 = *9

7^3 = **3

7^4 = ***1

7^5 = ****7

7^6 = *_**9

7^7 =____3

7^8 =____1

Repitation is occurring with interval of 4 .

so, for any integral value of "k"..

(***7)^(4k+1) ------- unit digit - 7

(***7)^(4k+2) ------- unit digit - 9

(***7)^(4k+3)-------- unit digit - 3

(***7)^(4k+4) ------ unit digit - 1

hence, unit digit of (347^42) = 9........(i)

similarly,

unit digit of (763219 ^ 2) = 1

unit digit of (53213 ^ 4) = 1

so, unit digit of the product = 1.......(ii)

so,

the required unit digit = 9 -1 = 8.......

hope , it helped.