Please help! Thanks!

Question

What is the ones digit in 3^50?

a. 1

b. 3

c. 7

d. 9

Answer 1

Try writing out the 1st 8 powers of 3.

3¹=3

3²=9

3³=27

3⁴=81

3⁵=243

3⁶=729

3⁷= a number with a units digit of 7

3⁸= a number with a units digit of 1

This pattern will repeat over and over for every 4 powers of 3: 3,9,7,1.

So if you divide 50 by 4, the remainder will tell you which exponent to apply to 3 to get its unit digit.

50/4 = 12 R 2. There are 12 complete patterns with 2 powers left over..

There is actually an operator (modulus) on a calculator that gives you the remainder. On Desmos it looks like this:

mod(50,4) = 2.

3²= 9, so the answer to the question is 9.