Can you find out ?
Algebra
Level
3
Find the digit at unit place
I believe you that you won't use any calculator.
9
2
8
7
5
3
6
4
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1 solution
7^1=7, 7^2=14, 7^3=343, 7^4=2401. The digits at units place are 7,4,3 and 1. The digits at the unit's place follow same pattern for the next powers of seven, i.e., 7^5=. . . . 7, 7^6=. . . . . 4, 7^7=. . . . . . .3, 7^8=. . . . . . . . 1. Therefore 7^95=. . . . . . . . . . . . . . . . . . . . . . . . . . 3. Similarly, 3^1=3, 3^2=9, 3^3=27, 3^5=. . 3, 3^6=. . . .9, 3^7=. . . . .7, 3^8=. . . . . . 1, 3^26=. . . . . . . . . . . . . . . . . 9. Now, 5 to the power any natural number (say n) will have 5 at the digit"s place. Hence, 5^11=. . . . . . . . . . . . . 5. So finally, 3-9+5=? The digit's place will never end with a negative number. So, 3-9=13-9=4. Finally,we get, 4+5 = 9.