How Do You Determine the Unit Digit of a^b?

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To determine the unit digit of a^b, one can analyze the unit digits of powers of a fixed base a while varying b. This approach reveals patterns in the unit digits that repeat periodically. For example, the unit digits of powers of 2 show a cycle: 2, 4, 8, 6. By identifying the cycle length and using the exponent b modulo this length, the corresponding unit digit can be determined. This method provides a systematic way to find the unit digit for any positive integers a and b.
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Hi, is there any way to find Unit Digit of a expression, say

a^b


where a, b, are positive integers?
 
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Yes.

Hint: fix a, vary b, and ignore the irrelevant details, see if you can find a clue...
 
U mean a pattern?

Like 2^2 = 4, like 2^2222 = 4? Because 2222 is divisible by 2?
 
I mean something a little more rigorous. :smile:

Consider the values of 2^1, 2^2, 2^3, ...
 

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