Question

The volume of a cube is 27 n Superscript 27cubic units. What is the length of one side of the cube?
3 n cubed units
3 n Superscript 9 units
27 n cubed units
27 n Superscript 9 units

Answer 1

We want s so that s^3 = 27 n^{27}. Take cube root:

s = (27 n^{27})^{1/3} = 27^{1/3} · n^{27/3} = 3 · n^9.

So the side length is 3 n^9 units.