Find the ratio of the sides of a cube with volume 512 m to a cube with volume 1728

First, to find the sides of a cube, you have to find the cube root.
For example, the cube root of 8 would be 2 because 2*2*2=8.
The cube root of 512 would be 8 and the cube root of 1728 would be 12.
Your ratio is 8:12, but now you need to simplify it.
Divide both sides by 4 and you would get 2:3.