Remember that a^b means a X a X ... a (b times). For example, 3⁴ = 3 X 3 X 3 X 3 = 81.

Write down 2¹, 2², 2³, 2⁴, 2⁵, 2⁶, 2⁷, 2⁸, 2⁹, 2¹⁰





Now write down the ones digit for 2¹, 2², 2³, 2⁴, 2⁵, 2⁶, 2⁷, 2⁸, 2⁹, 2¹⁰.





Do you see a pattern? Can you give a reason for the pattern?





Now write down the ones digit for 3¹, 3², 3³, 3⁴, 3⁵, 3⁶, 3⁷, 3⁸, 3⁹, 3¹⁰.





Now guess what the ones digit will be for the following:

2⁵⁰⁰⁰⁰

3¹²³⁴⁵

7⁴¹⁸³

486825^3685368

Now I have a new clock. When I first pick it up, the time is 4:00. I set the clock forward 3 hours, back 7 hours, ahead 56 hours, and back 13 hours. Then I set it forward 62 hours, and I do that 4 times. I set it back 77 hours 18 times. Then I set it forward 840 hours 179 times. What time will it be when I'm done?