The exact edge length of a cube is (5/2)^-2/3 units.

Question

Determine the volume of the cube.?

Answer 1

Length of the edge of a cube (s) = (5/2)^{( -2/3 )} units = (2/5)^{( 2/3)} units.

Volume of a cube (V) = s³ .

Substitute the value s = (2/5)^{( 2/3)} in V = s³.

V = [ (2/5)^{( 2/3)} ]³

= (2/5)^{( 2/3 * 3 )}

= (2/5)^{( 2)}

= 2² / 5²

= 4/25

= 0.16.

The volume of the cube is 0.16 cubic units.