What is the units (ones) digit of 7 to the 15th power?

Question

help! please give me a step by step explanation on how you figured this out please? thank you!

Answer 1

The digits of the powers of 7 are: 7, 9, 3, 1, 7, 9, 3, 1, ...

 

The 15th power shall have gone through the cycle 15/4, or 3 times with 3 remaining. The ones digit is 3.

Answer 2

7⁰ = 1

7¹ = 7

7² = 49

7³ = 343

7⁴ = 2401

7⁵ = 16807

note the last digit follows a pattern of 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, .... 

where 1, 7, 9, 3 is repeated forever

3 is the last digit when the exponent is 3, 7, 11, 15