What is the number in the unit place of the number (129)58?a)1b)2c)4d)9e)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Solution:

To find the unit digit of any power, we only need to know the unit digit of the base.

Let's find the unit digit of the base (129).

The unit digit of 129 is 9.

Now, we need to find the unit digit of (129)^58.

We can write (129)^58 as (129^4)^14 * (129^2).

Now, let's find the unit digit of (129^4).

The unit digit of 129^2 is 1 since 9^2 = 81.

Multiplying 1 by itself gives us 1. Hence, the unit digit of 129^4 is 1.

Now, let's find the unit digit of (129^4)^14.

The unit digit of (129^4)^14 is the same as the unit digit of (1)^14, which is 1.

Finally, we need to find the unit digit of (129^2).

The unit digit of 129^2 is 1 since 9^2 = 81.

Therefore, the unit digit of (129)^58 is the same as the unit digit of (129^2), which is 1.

Hence, the correct answer is option A, 1.

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