Question

Which equation finds the volume of a cube with a side length of 2n^6 units?

a.(2n^6)^3=8n^18 cubic units
b. (2n^6)^3=2n^18 cubic units
c. 2(n^6)^3=2n^18 cubic units
d. 2(n^6)^3=6n^18 cubic units

Answer 1

Explanation:

The answer is a

Answer 2

Given:

Side length of a cube is
`2n^6` units.

To find:

The equation for the volume of the cube.

Solution:

We know that, the volume of a cube is:

`V=a^3`

Where, a is the side length of the cube.

Putting
`a=2n^6`, we get

`V=(2n^6)^3`

`V=(2)^3(n^6)^3`
`[\because (ab)^m=a^mb^m]`

`V=8(n^(6* 3))`
`[\because (a^m)^n=a^(mn)]`

`V=8n^(18)`

So, the volume of the cube is
`(2n^6)^3=8n^(18)` cubic units.

Therefore, the correct option is A.