How do I tackle fractional powers?

The main thing to know when answering these sorts of questions is that the denominator of the fraction is the root you take of the given number. For example, 16^1/2 is the same as the sqaure root of 16, which is 4. Or 125^1/3 is the cube root of 125 which is 5. However, if the numerator is not 1 then there is more to consider: Take x^2/3 for example: We know from laws of indices that x^2/3 is the same as (x^1/3)² because when you raise one power to another power, you multiply them together. Once we have done this, the question becomes much simpler; you first take the cube root of x, and then square it. e.g. 'What is 81^3/4?' Consider it as (81^1/4)³: First take the bit in the brackets, which is equal to 3. Then cube this result which is equal to 27. So the answer is 27.