Find the digit in the units place of the
integer 3^444

Can someone help me solve this.Its not for a test,Im just trying to gain some extra credit points

Question

Find the digit in the units place of the
integer 3^444

Can someone help me solve this.Its not for a test,Im just trying to gain some extra credit points

anonymous · Answer

look at the pattern of three to powers

anonymous · Answer

$$3^0=1\
3^1=3\
3^2=9\
3^3=27\
3^4=81$$  now look only at the ones place

anonymous · Answer

$$3^0\to 1\
3^1\to 3\
3^2\to 9\
3^3\to 7\
3^4\to 1$$
once you see a 1 the pattern will repeat

anonymous · Answer

ok i get it but how is 3^4=1??

radar · Answer

That was what the "ones" or units value, 3^4 was 81, 1 is in the unit position 8 was in the tens position.

anonymous · Answer

@radar Im still lost

radar · Answer

He was suggesting you study the pattern, noting when the exponent ended in 4 the result was with a 1 in the for the units digit$$3^{4}=81$$
$$3^{8}=6561$$
$$3^{12}=531441$$$$3^{16}=43046721$$
Do you get the pattern?  Note that the value of the units digit is a 1........so just maybe we could just say that $$3^{444}=$$a very large value whose units digit is a 1.

radar · Answer

*"ending in 4 or a multiple of 4"