Determine the remainder when

Question

$1025^{1005}\equiv x(1023)$

I did:

$1025\equiv 2(1023)$

$1025^{1005}\equiv 2^{1005}(1023)$

I don't know the next step.

Answer 1

\begin{align} 2^{1005} &\equiv (2^{10})^{100}\cdot 2^5\pmod{1023} \\ &\equiv (1)^{100}\cdot 32 \pmod{1023} \\ &\equiv 32 \pmod{1023} \end{align}