Let's analyze the problem step-by-step. Given:

• nnn is a whole number.
• When nnn is divided by 4, the remainder is 3.

This means we can write:

n=4k+3n=4k+3n=4k+3

for some integer kkk.

Step 1: Express 2n2n2n

Multiply both sides of the equation by 2:

2n=2(4k+3)=8k+62n=2(4k+3)=8k+62n=2(4k+3)=8k+6

Step 2: Find the remainder when 2n2n2n is divided by 4

Divide 2n2n2n by 4:

2n=8k+6=4(2k)+62n=8k+6=4(2k)+62n=8k+6=4(2k)+6

When dividing by 4, the term 4(2k)4(2k)4(2k) is divisible by 4 and leaves no remainder. So, the remainder depends on 6 modulo 4:

6÷4=1 remainder 26\div 4=1\text{ remainder }26÷4=1 remainder 2

Answer:

The remainder when 2n2n2n is divided by 4 is 2.