What is the value of 64^(2/3)?

The index is 2/3 so first of all we can separate this and begin by looking at the 1/3. Fractions as indices mean that you must root the number, in this case we must cube root it because of the 3 in the denominator (bottom) of the fraction. Now cube rooting 64, if we do not notice it straight away we can try out a few numbers to see if we can reach it. We can start at 2- 2 times 2 times 2 is 8 so that is not the cube root of 64. Now we can try 3- 3 times 3 times 3 is 27 so that is not it either, Next we can try 4- 4 times 4 times 4 is 64 so we can conclude that the cube root of 64 is 4. So now we must move on to the second part of the index which is the squaring part, so finally we take 4 and square it. 4 times 4 is 16 so overall our answer of 64^(2/3) is 16.