Part A. Solve the following problem.
What is the last digit of 2^1999?

Part B. Write up a solution to the problems above using the following five step process.

1. State the problem. Explain in detail what the problem means and is asking you to find.

2. Describe the strategy you used to solve the problem.

3. Show the details of how you carried out the plan to solve the problem.

4. Explain how you know your answer is correct/makes sense.

5. Create a new question based on the one you just solved. You don't have to solve the new problem

I’m begging anyone pls

To find the last digit of [tex]2^{1999}[/tex], we can observe a pattern in the last digits of powers of 2. The last digit of powers of 2 repeats every 4 powers:

[tex]2^1 = 2[/tex] ends in 2
[tex]2^2 = 4[/tex] ends in 4
[tex]2^3= 8 [/tex] ends in 8
[tex]2^4= 16[/tex] ends in 6
[tex]2^5 =32 [/tex] ends in 2
[tex]2^6 = 64[/tex] ends in 4 (and the cycle repeats)

Since [tex]1999[/tex] is one less than a multiple of 4 ([tex]1999 = 4 \times 499 + 3[/tex]), the last digit of [tex]2^{1999}[/tex] is one position before the end of the cycle, which is 8.

[tex]\dotfill[/tex]

Part B:

Step 1:

State the problem:

Find the last digit of [tex]2^{1999}[/tex].

[tex]\dotfill[/tex]

Step 2:

Describe the strategy:

Recognize the cyclical pattern of the last digits of powers of 2. Since 1999 is one less than a multiple of 4, we know the last digit will be the third one in the cycle.

[tex]\dotfill[/tex]

Step 3:

Details of the solution:

The cycle repeats every 4 powers, so divide the exponent by 4 to find the position in the cycle:

[tex] 1999 = 4 \times 499 + 3 [/tex]

So, the last digit is the third one in the cycle, which is 8.

[tex]\dotfill[/tex]

Step 4:

Explain correctness:

The pattern holds true, and the result aligns with the observation that [tex]2^3[/tex] ends in 8.

[tex]\dotfill[/tex]

Step 5:

Create a new question:

What is the last digit of [tex]3^{2023}[/tex]?