How do you work out question 10 in zahada?

Zahada Question 10: Find the last four digits of the number:

$$(2023)^{2024}$$

Solution:

Since the last digit of 2023 is 3, the last digit of (2023)^n will always be 3 for any positive integer n.

In addition, any power of 10 will result in a number with a 0 in the last digit. Any power of 4 will result in a number with a 4 in the last digit.

So we need to find the highest power of 4 such that dividing 2024 by this power results in a quotient with a 0 in the last digit.

We have:

$$2024 \div 4 = 506 \text{ (remainder 0)}$$

So the highest power of 4 dividing 2024 with a quotient ending in 0 is 4 itself.

Hence the last four digits of (2023)^2024 are 7083.