The side length of a cube can be represented by the expression 2x^5. If the side length is doubled wirite an expression to represent the new volume of the cube

Answer 1

Lets represent the side length with s

s = 2x^5

If this side length is being doubled, our new equation for the side length is

2s = 2*2x^5 = 4x^5

We are going to write the volume equation by putting 4x^5 where the side length should go.

V = side^3

V= (4x^5)^3

Power of a product law —> outer exponent multiples onto each inner exponent. (Remember 4 is really 4^1)

4^1–> 4^1*3 = 4^3

x^5–> x^5*3=x^15

V = 4^3 * x^15

The last step would be to simplify 4^3

4^3 = 4*4*4=64

V = 64x^15