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:The expression which represents the New Volume of cube is [tex]64x^{15}[/tex].Step-by-step explanation:Given:Side length of cube(a) = [tex]2x^5[/tex]Now Given that side length is doubled.It means that the given side length is multiplied with 2.New side length of cube (a) =  [tex]2 \times 2x^5 = 4x^5[/tex]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 = [tex]a^3[/tex]Now Substituting the value of a as new side length we get;New Volume of cube =[tex](4x^5)^3 = (4)^3(x^5)^3[/tex]Now Using Law of Indices which states [tex](x^a)^b=x^{ab}[/tex]Therefore New Volume of cube = [tex]64x^{15}[/tex] Hence, The expression which represents the New Volume of cube is [tex]64x^{15}[/tex].