what will be the remainder in following scenario?

Question

what will be the method or efficient method to find remainder when $2^{70}$ divided by 96.

I convert it into $2^{65}$ /3 and evaluated remainder as (-1)+3=2 but this is not the desired answer , so help me to fix this.

Answer 1

You have $2^{65}= 3n+2$

Multiplying by 32 you get

$ 2^{70}=96n +64$

So $2^{70} \equiv 64$ (mod 96)