Is this procedure for $5^{300} \bmod 11$ correct? I'm new to modular exponentiation. Is this procecdure correct?
$$5^{300} \bmod 11$$

$$5^{1} \bmod 11 = 5\\
5^{2} \bmod 11 = 3\\
5^{4} \bmod 11 = 3^2 \bmod 11 = 9\\
5^{8} \bmod 11 = 9^2\bmod 11 = 4\\
5^{16} \bmod 11 = 4^2 \bmod 11 = 5\\
5^{32} \bmod 11 = 5^2 \bmod 11 = 3$$

$$5^{300} = 3 + 3 + 3 + 3 +3 +3 + 3 + 3 +3 +4 + 9$$

You could also notice $11$ is prime, so by Fermat's Little Theorem $ 5^{10}\equiv 1 \bmod 11$
from here we get $5^{300}=(5^{10})^{30}\equiv1^{30}\equiv 1 \bmod 11$
