Calculator!
When you have a nth root of a term to the xth power, you can rewrite it in the form of 256^(x/n)=(nth root of 256)^x Now you can simplify the radical and then raise it to the x power.
Your n=8 and x=2 so the notation isn't confusing.
First of all you need to recognise that 256 = 2^8. (It is a really good idea to know all the powers of 2 up to 2^10 as they always crop up in problems. Also learn all the powers of 3 up to 3^5. It makes life with indices so much easier.
Replace 256 with 2^8. Replace the 8th root symbol with ^(1/8) so you have ((2^8)^2)(1/8).
Then use your index law that says (a^m)^n = a^mn and you will have your answer!!
DON'T TOUCH YOUR CALCULATOR!!