Question

When 39 is raised to the 100th power, the unit's digit of the answer will be?​

Answer 1

The unit's digit of 39 raised to the 100th power is 9.

Explanation:

• The unit digit of 39 is 9.
• So, divide the power 100 by 9.

⇒ 100/9 = 11 and (remainder = 1)

Now check the unit digits of multiples of 9.

`9^(1)` = 9 ⇒ unit digit = 9

`9^(2)` = 81 ⇒ unit digit = 1

`9^(3)` = 729 ⇒ unit digit = 9

`9^(4)` = 6561 ⇒ unit digit = 1

• The unit digit repeats as 9 for odd power and 1 for even power.
• The remainder of 100/9 is 1, which is a odd number.
• Therefore, the unit digit of
  `39^(100)` = 9