The volume of a cube-shaped box is ##27^5## cubic millimeters. What is the length of one side of the box?

I found: ##243mm##

Consider the cube of side length ##x##. The volume will be equal to ##x^3##. So if we have the entire volume, ##V=27^5##, we can take the cube root of it to get the side length: ##x=root3(27^5)=243mm##

To check it we can try: ##V=243^3=14,348,907mm^3=27^5mm^3##