Predicting the value of the ones places.?

Question

Use a repeating pattern to find the numeral that will be in the ones place of 2 to 387power. I'm totally lost. Can anyone help me?

Answer 1

Consider the following:

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
2^9 = 512
2^10 = 1024

Look at the ones place in each number. You should see the following pattern:
2, 4, 8, 6, 2, 4, 8, 6, 2, 4...

It simply repeats 2, 4, 8, 6 over and over. Whenever the exponent is a multiple of 4, the ones place is a 6. So, we just need to find where 387 is in this cycle. Using division to find the remainder of 387/4, we get 3. This means 384 is a multiple of 4, so 2^384 ends in a 6, and 387 is 3 greater than a multiple of 4, so 2^387 ends in an 8.