unit digit into 12 to the power 786 + 17 to the power 756 + 19 to the power 3 43 + 89 to the power 133
Answers
Given : 12⁷⁸⁶ + 17⁷⁵⁶ + 19³⁴³ + 89¹³³
To find : unit digit
Solution:
12⁷⁸⁶ + 17⁷⁵⁶ + 19³⁴³ + 89¹³³
12⁷⁸⁶ = 12² * 12⁷⁸⁴
= 12² * 12⁴ˣ¹⁹⁶
= 12² (12⁴)¹⁹⁶
2⁴ end with 6 , 6¹⁹⁶ ends with 6
2² ens with 4
6 * 4 ends with 4
12⁷⁸⁶ ends with 4
17⁷⁵⁶ = (17⁴)¹⁸⁹
7⁴ ens with 1
1¹⁸⁹ ends with 1
17⁷⁵⁶ ends with 1
19³⁴³ = 19 * (19²)¹⁷¹
9² ends with 1
1¹⁷¹ ends with 1
19 * 1 ens with 9
19³⁴³ ends with 9
89¹³³ = 89 * (89²)⁶⁶
9² ends with 1
1⁶⁶ ends with 1
89 * 1 ens with 9
89¹³³ ends with 9
12⁷⁸⁶ + 17⁷⁵⁶ + 19³⁴³ + 89¹³³ ends with
4 + 1 + 9 + 9
= 23
Ends with 3
12⁷⁸⁶ + 17⁷⁵⁶ + 19³⁴³ + 89¹³³ ends with 3
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