elementary number theory - Find the remainder $4444^{4444}$ when divided by 9

Find the remainder $4444^{4444}$ when divided by 9

When a number is divisible by 9 the possible remainder are $0, 1, 2,3, 4,5,6,7,8$ we know that $0$ is not a possible answer. My friend told me the answer is $7$ but how

I am thinking of taking 4444 divide by 9 and that left a remainder of 7 so $4444 \cong 7$ mod 9 based on that I am guessing $4444^{4444} \cong 7^{4444}$ mod 9 so to me no matter how big the power is that will still be a remainder of 7 is that correct to think like that