Unit Digit in 7¹⁰⁵
The unit digit in a number is the digit that appears in the ones place of the number. To find the unit digit in a large exponent like 7¹⁰⁵, we need to understand the concept of cyclicity of the unit digit of numbers.

Important Formulas: Number System
When we raise a number to a power, the unit digit of the result follows a cyclical pattern. For example, when we raise 7 to different powers, the unit digit follows the pattern: 7¹ = 7, 7² = 9, 7³ = 3, 7⁴ = 1, and then repeats with 7⁵ = 7, 7⁶ = 9, and so on.

Explanation
To find the unit digit in 7¹⁰⁵, we need to determine the pattern the unit digit of 7 follows. Since the cyclical pattern of the unit digit of 7 repeats every 4 powers, we can reduce the exponent 105 to the equivalent power mod 4 as follows:
105 mod 4 = 1
This means that 7¹⁰⁵ will have the same unit digit as 7¹, which is 7.
Therefore, the unit digit in 7¹⁰⁵ is 7.