Question

the side length of a cube can be represented by the expression 2x^5. if the side length is doubled, write an expression to represent the new volume of the cube.

Answer 1

The expression which represents the New Volume of cube is
`64x^(15)`.

Explanation:

Given:

Side length of cube(a) =
`2x^5`

Now Given that side length is doubled.

It means that the given side length is multiplied with 2.

New side length of cube (a) =
`2 * 2x^5 = 4x^5`

Now We need to find the volume of cube with the new side length.

We know that Volume of a cube is equal to cube of side length.

Hence framing in equation form we get;

New Volume of cube =
`a^3`

Now Substituting the value of a as new side length we get;

New Volume of cube =
`(4x^5)^3 = (4)^3(x^5)^3`

Now Using Law of Indices which states
`(x^a)^b=x^(ab)`

Therefore New Volume of cube =
`64x^(15)`

Hence, The expression which represents the New Volume of cube is
`64x^(15)`.