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.

Step-by-step 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