What is the unit digit in 189^723? A] 7 B] 9 C] 1 D] 3 Options : A B C D

The unit digit of a number raised to a power can be found by looking at the cyclicity of the unit digit.

The number 189 ends in 9. The digits 0, 1, 5, and 6 always have the same unit digit when raised to a power. The digits 2, 3, 7, and 8 have a cyclicity of 4, and the digits 4 and 9 have a cyclicity of 2.

Since 189 ends in 9, we look at the cyclicity of 9, which is 2. The powers of 9 alternate ending in 9 and 1.

To find out which one is the unit digit of 189^723, we need to look at the remainder of 723 divided by 2 (the cyclicity of 9).

723 divided by 2 gives a quotient of 361 and a remainder of 1.

This means that the unit digit of 189^723 is the same as the unit digit of 9^1, which is 9.

So, the unit digit in 189^723 is 9.

Therefore, the answer is B] 9.