Which expression is a perfect cube?

A:12x^12 y^18

B:12x^27 y^125

C:64x^15 y^18

D:64x^27 y^125

The expression that is a perfect cube is D. Because to determine the side length of a cube we would need to take the cube root of the number and the variables and unlike the other answers we can't take the cube root out perfectly. For D though the side length is calculated by taking the cube root of 64, which is 4, cube root of x^27 which is x^3, and cube root of y^125 which is y^5. Putting everything together the side length should be 4X^3Y^5. Multiplying this expression by itself 3 times will give you what you started out with.