discrete mathematics - How to solve a congruence with Euclidean algorithm with exponents

I need help solving this particular congruence with Euclidean algorithm. I, in general, don't know how to solve congruences with exponents so I don't even know how to start.

\begin{align*}
x \equiv 6^{29} \;(\bmod\; 7)
\end{align*}

I know how to solve the ones without exponents, so it would be great if someone could do a step by step solution for this example and explain it to me a little bit better. I want to use Euclidean algorithm because that's how I learnt to do all other congruences and Chinese remainder theorem. (This is how i do them: https://www.youtube.com/watch?v=4-HSjLXrfPs)

Any help is much appreciated.