What is the number in the unit’s place of 999^22292582Options :9371

The question is asking for the digit in the unit's place of the number obtained when 999 is raised to the power of 22292582.

To solve this, we need to understand the pattern of the last digit of powers of 9.

The pattern for the last digit of powers of 9 is as follows: 9, 1, 9, 1, 9, 1, and so on. This pattern repeats every 2 powers.

So, for any even power of 9, the last digit will be 1.

Since 22292582 is an even number, the last digit of 999^22292582 will be 1.

So, the number in the unit’s place of 999^22292582 is 1.

The number in the unit's place of 999^22292582 is 1.

Here's the step-by-step explanation:

1. First, we need to understand the cyclicity of 9. The cyclicity of 9 is 2, which means the last digit repeats every 2 powers. The cycle is {9,1}.

2. Then, we need to find the remainder when the power (22292582) is divided by the cyclicity (2). The remainder is 0.

3. Since the remainder is 0, we take the last number in the cycle of 9, which is 1.

So, the number in the unit's place of 999^22292582 is 1.