MathRevolution wrote:
Que: If n is positive integers, what is the unit digit of \((3^{4n+1})(4^{19})\)?
A. 1
B. 2
C. 4
D. 6
E. 8
Solution: Powers that repeat every 4th power:Ex) Units digit: The digit 3 repeats after every fourth power
=> \(3^1= ~3, ~3^2= ~9, ~3^3 = ~7, ~3^4= ~1, ~3^5= ~3, ... \)
=> Pattern: 3, 9, 7, 1, 3, 9, 7, 1 ….
Ex) Units digit: The digit 4 repeats after every second power
=> \(~4^1 = ~4, ~4^2 = ~6, ~4^3 = ~4, ... \)
=> Pattern: 4, 6, 4, 6…
We have to find the units digit of (34n+1)(419) if n is positive integers
=> \((3^{4n+1})(4^{19})\)
=> \((3^4 )^n * 3^1 *(~4)\)
=> \((81)^n* 3^1 *(~4) =(~1)* 3^1 *(~4) =(~2)\)
Therefore, B is the correct answer.
Answer B _________________