I don't understand how to simply this:
$\displaystyle \sqrt[8]{256^2}$
The answer is 4 but I don't know how to work out the solution to get to 4.
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!!