Work out the cube root of (64x1000).

We are asked to calculate (64x1000)^1/3. We can use the laws of indices to write that expression as 64^1/3x1000^1/3, which is easier to evaluate. To work out 64^1/3, we either spot the answer as 4 or take an initial guess and then improve on it. Say we initially guess that the answer is 3. We then check by cubing 3 so we get 3³=27 - our answer is too small. When we try the same with 4 we see that we are correct. To work out 1000^1/3 is a lot simpler as we can immediately see that 1000 is a power of 10, so 10 would be a reasonable guess and indeed 10³=1000. We can now evaluate the original expression as 4x10=40.