Value of $7^{64}$

Question

How to find the value of $7^{64}$ ?

Anyone know the simple way to find the value of $7^{64}$ and is it possible to use that way to find another integer exponential ?

Answer 1

If you want to perform the least amount of calculation (it will still be a lot to do by pen and paper), you should use the fact that

$$7^{64} =\left(\left(\left( \left(\left(7^2\right)^2\right)^2\right)^2\right)^2\right)^2$$

So, you only need to perform $6$ operations.

1. First, you square $7$.
2. Then you square the result.
3. Then you square the result.
4. Then you square the result.
5. Then you square the result.
6. Then you square the result.