Question

use inductive reasoning to determine the units digit of the number 2^44

the unit digit of 2^44 is_____

powers of 2-
2^1=2
2^2=4
2^3=8
2^4=16
and so on that last one they have is 2^12

so 2^44 would be 1.7592188?

Answer 1

You started off ok, but then your logic exploded.

You only have to consider the unit digit

listing only the unit digit:
2^1 -- 2
2^2 -- 4
2^3 -- 8
2^4 -- 6
2^5 -- 2
2^6 -- 4
2^7 -- 8
2^8 -- 6
.... notice they cycle 2,4,8,6
If the exponent is evenly divisible by 4, the last digit is 6
- (if the unit digit is even, but not divisible by 4, the last digit is 4)