discrete mathematics - modulo of a large number

I need help with solving modulo of large numbers, wondering if it is possible to compute the answer without the use of calculator.

for example: 545^112 (mod 23) how can this be solved?
I reduced my answer to 545^2 (mod 23) and wonder if there is a way to continue without the use of calculator to compute 545^2.

and how can I find 545^112 (mod 24) from here?

Thanks.