What to the power of four equals 256

A good way to determine this is to use logarithms, the inverse of exponents.
In any given equation, if y=b^x, then logbase(b) of y = x

Due to a property of logarithms, you can also write logbase(b) of y as logy/logb.
The "log" button can be found easily on most modern calculators, so you can follow along too.
Anyways, though, our problem says that 256 = b^4
You can apply logarithms, but an easier way to do this is to square-root 256 twice. 
sqrt256->16
sqrt16->4
4^4 is 256. Let's check, shall we?
4*4 is 16. That *4 is 64. 64 *4 is... 256!
Those are just a couple ways to go about it, though.