Hi Candice,

I'm going to compute powers of 3 and record them in a table but only record the ones digit.

power of 3	ones digit
1	3
2	9
3	7
4	1
5	3
6	9
7	7
8	1
9	3

What I see is that the ones digits are repeating in a pattern, 397139713971···. The pattern is 3971 and hence the pattern length is 4 digits.

So what would the table above look like if I extended it to 79 rows?

79 divided by 4 is 19 with a remainder of 3 so the pattern would repeat 19 times and then there would be 3 more rows. The ones digits in these three rows are 3, 9 and 7 so the ones digit of 3 to the 79 is 7.

power of 3	ones digit
1	3
2	9
3	7
4	1
.	.
.	.
73	3
74	9
75	7
76	1
77	3
78	9
79	7

Penny