Posted by **bethel** on Monday, June 18, 2012 at 4:58pm.

If 3 is raised to the 59th power, i.e. 359, what is the units digit? The units digit is the digit in the ones place. Explain the method used to find your answer.

- algebra math -
**MathMate**, Monday, June 18, 2012 at 5:55pm
3^{1}=3

3^{2}=9

3^{3}=27

3^{4}=81

3^{5}=243

...

So we conclude that 3 raised to any power divisible by 4 ends with a 1.

Similarly, 3 raised to any power "divisible by 4 minus one", such as 3, 7, 11, ... ends with a 7.

Can you figure out the answer for 3^59 (noting that 59=4*15-1)?

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