What is the unit digit of the number \((22)^{23}\)

Step 1: Focus on unit digit

Unit digit of 22 is 2, so find unit digit of:

$2^{23}$

Step 2: Pattern of $2^n$ (unit digits)

$2^1 = 2$
$2^2 = 4$
$2^3 = 8$
$2^4 = 6$

Cycle repeats every 4: 2, 4, 8, 6

Step 3: Find position

$23 \mod 4 = 3$

So take 3rd term in cycle → 8

Final Answer: 8