Question

if i raise 4 to the 214th power, whats the units digits?of the result?

Answer 1

You'll want to use modular arithmetic here. In particular, you want to know:
$$4^{214}\pmod{10}$$Is this something you have seen before?

Answer 2

If not thats fine, this can be explained without using modular arithmetic. Its just a little easier to explain with it.

Answer 3

i plugged 4^214 the answer is 6.931.674e the unite digit should be 6

Answer 4

i think

Answer 5

maybe im mistaking something

Answer 6

Just try the first few powers and see if you spot a pattern in the ones digits:
$$4^1=4$$$$4^2=16$$$$4^3=64$$$$4^4=256$$$$4^5=1024$$$$4^6=4096$$

Answer 7

\[\large 4^{214} = 16^{107}\]

16 maybe easier to work

Answer 8

thanks