Calculate 64^2/3. (No calculator)

64^2/3 may seem difficult to calculate at first but really boils down to two simple steps. This is because 64^2/3 = (64^1/3)². This shows we can first do the operation inside of the brackets, followed by the outside operation, to obtain the answer. 64 to the power of a third is equal to the cube root of 64. This means the answer is much smaller than 64, and by trial and error of cubing small numbers (2 = 8 etc.) we find that this is equal to 4. Why something to the power of a third is the same as a cube root is best explained by considering the reverse operation. The cube root can be defined as an operation on a cubed number to return it to its original value. We also know that (4³)^1/3 = 4¹ = 4, which proves the above statement. Now all we have to do is the second part of the operation, which is 4² = 16. Therefore the answer is 16. (N.B. If we had swopped the order of the two steps (i.e. (64²)^1/3), this would've given the same result but it is unnecessarily difficult to calculate 64 squared then take its cube root.)