Congruence 10 modulo 7 I'm reading some proofs for divisibility rules and see that $10 \equiv -1 \pmod{11}$, then $10^2 \equiv 1 \pmod{11}$ and etc., it's clear for me, but I can't understand the situation with modulo 7. If we have $10 \equiv 3 \pmod{7}$ how can we get the rest of the values? They are $10^2 \equiv 2 \pmod{7}$, $10^3 \equiv -1 \pmod{7}$ and etc. 
I'm sorry if it's a stupid question, but I want to figure out this very well.

As a start, we use the rule that 
$$a \equiv b \pmod{n} \Rightarrow a^k \equiv b^k \pmod{n},\forall k\in \mathbb{N} \tag{1}$$
Hint
$$10 \equiv 3 \pmod{7} \Rightarrow 10^2 \equiv 3^2 \pmod{7} \Rightarrow \\
10^2 \equiv 9\equiv 7+2\equiv 2 \pmod{7}$$
or
$$10^3 \equiv 3^3 \pmod{7} \Rightarrow \\
10^3 \equiv 27\equiv 28-1\equiv 4\cdot7-1\equiv -1 \pmod{7}$$
