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.
[tex]9^{1}[/tex] = 9 ⇒ unit digit = 9
[tex]9^{2}[/tex] = 81 ⇒ unit digit = 1
[tex]9^{3}[/tex] = 729 ⇒ unit digit = 9
[tex]9^{4}[/tex] = 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 [tex]39^{100}[/tex] = 9
