How to find $a^b$, where $a$ and $b$have more than $10$ digits?

Question

Consider any two numbers $a$ and $b$ of more than 10 digits, how to find $a^b$ (without the aid of computing devices). Is there any shortcut method to do it. other than binomial series. How do I solve this?

Answer 1

If $a$ and $b$ both have more than $10$ digits, $a^b \ge (10^{10})^{(10^{10})}=10^{(10^{11})}$, so it has more than $100,000,000,000$ digits. You won't be working it out by hand. Maybe you are supposed to work out $a^b \bmod$ something?