Math Help?

Question

What is the ones digit when 9^55 is expressed as an integer?

^ means to the power like 2 squared

Please Show Work!

Me soooooooo confused....4 or 9?

Answer 1

Even powers are 1 and odd powers are 9

9 squared is 81
9 cubed is 729

55 is odd so this is 9.

Write the series out to convince yourself

Answer 2

Hi Victor,
9^1 = 9
9^2 = 81
9^3 = 729
9^4 = 6511
Notice that a pattern continues and that the even powers of 9 end in 1, the odd powers of 9 end in 9. Thus your answer will end in 9 (ones digit). Hqave a great week.
Thanks,
Eds


.

Answer 3

Completely agree with Jay
9^1 = 9
9^2 = 81
9^3 = 729

even powers end with 1
odds end with 9
55 is odd so 9 is the ones digit

Answer 4

4

Answer 5

Let x=9^55, and consider x mod 10:

9^55 = (-1)^5 (mod 10)
=-1 (mod 10)
= 9 (mod 10),
so x mod 10 = 9, or in other words, the ones digit of x is 9.

(I have no idea why everybody jumped on the 4's bandwagon, but they're pulling your leg!)

Answer 6

4

Answer 7

even powers of 9 end in 1, odd powers end in 9
55 is odd, therefore 9^55 ends in 9

to demonstrate, start with 9^1 and multiply by 9, but stop your multiplication after you've calculated the one's digit. you'll get the sequence as explained above:

9, 1, 9, 1, 9, 1, 9, etc.
(all you need to know is 9*9 is 81, and 9*1 is 9)

Answer 8

9^1 = 9
9^2 = 81
9^3 = 729

even powers end with 1
odds end with 9
55 is odd so 9 is the ones digit

the last number is cyclic. i dont see how people can get 4

Answer 9

The answer is 4

Answer 10

Im sure thats it 4 but i cant how the work
sorry