find the unit digit of (7592)^56789+(6543)^12345
Answers
Answer:
find the unit digit of (7592)^56789+(6543)^12345 =5
The Unit Digit of (7592)⁵⁶⁷⁸⁹+(6543)¹²³⁴⁵ is 5
Explanation:
Given:
(7592)⁵⁶⁷⁸⁹+(6543)¹²³⁴⁵
To find:
The Unit Digit
CYCLITY:
Number Cyclicity
1 1
2 4
3 4
4 2
5 1
6 1
7 4
8 4
9 2
Step1: Find the Unit Digit for (7592)⁵⁶⁷⁸⁹
==> 7592, the last digit is 2
==> l=2
==> The cyclicity of 2 is 4
==> The power value is 56789
==> 56789÷4
==> 56789 is not divisible by 4
==> 56788 is divided by 4. So, the remainder is 1
==> The remainder is 1
==> let remainder be x
==> x= 1
==> To find unit digit, lˣ
==> l = 2 and x=1
==> lˣ= 2¹
==> The unit digit of (7592)⁵⁶⁷⁸⁹ is 2
Step2: Find the Unit Digit for (6543)¹²³⁴⁵
==> 6543, the last digit is 3
==> l=3
==> The cyclicity of 3 is 4
==> The power value is 12345
==> 12345÷4
==> 12345 is not divisible by 4
==> 12344 is divided by 4. So, the remainder is 1
==> The remainder is 1
==> let remainder be x
==> x= 1
==> To find unit digit, lˣ
==> l = 3 and x=1
==> lˣ= 3¹
==> The unit digit of (6543)¹²³⁴⁵ is 3
Step3: Find the Unit Digit of (7592)⁵⁶⁷⁸⁹+(6543)¹²³⁴⁵
==> The unit digit of (7592)⁵⁶⁷⁸⁹ is 2
==> The unit digit of (6543)¹²³⁴⁵ is 3
==> (7592)⁵⁶⁷⁸⁹+(6543)¹²³⁴⁵ = 2+3
==> (7592)⁵⁶⁷⁸⁹+(6543)¹²³⁴⁵ = 5
==> The Unit Digit of (7592)⁵⁶⁷⁸⁹+(6543)¹²³⁴⁵ is 5