What is the remainder when $\large 4444^{4444}$ is divided by $\large 9$?

Question

anonymous · Answer

start taking digital remainders

anonymous · Answer

in the exponents $4+4+4+4=16$  and $1+6=7$ so the remainder when you divide $4444$ by $9$ is $7$

anonymous · Answer

therefore the remainder of $4444^{4444}$ when divided by $9$ is the same as the remainder of $7^7$ when divided by $9$

anonymous · Answer

you  have some more work to do to finish, but i hope that part was clear enough

anonymous · Answer

well not much actually 
$$7^7=49^3\times 7$$ should finish it up nicely

anonymous · Answer

i see :)
Thank you

ganeshie8 · Answer

nice :) 

$$\large 4444^{4444}  \equiv   (4\times  11\times  101)^{4444}  \equiv   2^{4444} \mod  9$$