What is the unit digit of 7777^3333-3333^7777, give the answer with the explanation

• 7^3333=(7^4)^833*7=7
  As cyclicity of 7is 4 so 7^4=1
  3^7777=(3^4)^1944*4=4
  As cyclicity of 3 is 4 so3^4=1
  7-4=3 is the and.
• 9 years agoHelpfull: Yes(0) No(0)
• Ans is 4
  7777^1...unit digit is 7 as 7^1
  7777^2...unit digit is 9 as 7^2
  7777^3...unit digit is 3 as 7^3
  7777^4...unit digit is 1 as 7^4
  7777^5...unit digit is 7 as 7^5. Hence after every forth power unit digit cycle is repeated.
  (7777^3332)*(7)=(unit digit is 1)*7=7
  3333^1.....unit digit is 3 as 3^1
  3333^2.....unit digit is 9 as 3^2
  3333^3.....unit digit is 7 as 3^3
  3333^4.....unit digit is 1 as 3^4
  3333^5.....unit digit is 3 as 3^5. Hence after every forth power unit digit cycle is repeated.
  (3333^7776)*3=(unit digit is 1)*3=3
  Hence 7-3=4
• 9 years agoHelpfull: Yes(0) No(0)