manhattan gmat

Enginpasa1 wrote:17^27 has a units digit of:

1
2
3
7
9


qa is 3 but i chose 9.

Here is my reason for choosing 9. 17 end in 7 and power of 27 end is 7 therefore I multipplied them together. THis technique I learned from the manhattan gmat lesson. THe corect way is to find the sequence pattern and count up to 27. why did i do mine wrong i wanted to use the manhattan way. can someone show me where i went wrong.

We only care about the last digit, so let's just think about 7^27.

Let's look at the pattern of 7s:

7^1 = 7
7*7 = ..9
7*9 = ..3
7*3 = ..1
7*1 = ..7

and so on.

So, powers of 7 will cycle through 4 final digits: 7, 9, 3 and 1.

We want the 27th term in the series. Since we have a cycle of 4 terms, we really have 24 terms (which would put us at 1, the 4th ending of the cycle) + 3 more terms. The 3rd "final digit" in the cycle is 3, so that's the right answer.