Given:
Side length of a cube is [tex]2n^6[/tex] units.
To find:
The equation for the volume of the cube.
Solution:
We know that, the volume of a cube is:
[tex]V=a^3[/tex]
Where, a is the side length of the cube.
Putting [tex]a=2n^6[/tex], we get
[tex]V=(2n^6)^3[/tex]
[tex]V=(2)^3(n^6)^3[/tex] [tex][\because (ab)^m=a^mb^m][/tex]
[tex]V=8(n^{6\times 3})[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]V=8n^{18}[/tex]
So, the volume of the cube is [tex](2n^6)^3=8n^{18}[/tex] cubic units.
Therefore, the correct option is A.
