What is the unit digit of the expression 2^{44}? — State PSC Exam

What is the unit digit of the expression $2^{44}$ ?

A
1
B
2
6Answer
D
8

Answer

The unit digit of

2^{44}

is 6.

The unit digit of powers of 2 repeats in a pattern of 4 steps: 2, 4, 8, 6. Dividing the exponent 44 by 4 yields a remainder of 0. A remainder of 0 means the full 4th power in the cycle applies, so

2^4 = 16

yields a unit digit of 6.

Step-by-Step Solution

Identify the base and its cyclicity pattern.

The base is 2. The powers of 2 follow a cyclic pattern of unit digits:

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

(unit digit 6). The cyclicity of 2 is 4.

Unit digits repeat in a fixed pattern of length 4 for base 2.

Divide the exponent by the cyclicity period.

44 \div 4 = 11

with a remainder of

0

Determining the remainder tells us which position in the 4-step cycle applies.

Apply the cyclicity rule for remainder 0.

A remainder of 0 corresponds to the 4th power in the cycle (

2^4 = 16

), giving a unit digit of 6.

When the exponent is exactly divisible by the cyclicity length, the unit digit is determined by the last element of the cycle (

2^4

), not

2^0

Key Concept

Unit Digit Cyclicity for Base 2

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