Question

1. 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.

Explanation:

Step1: Find the new side - length

The original side - length of the cube is $2x^{5}$. When it is doubled, the new side - length $s$ is $2\times(2x^{5}) = 4x^{5}$.

Step2: Recall the volume formula for a cube

The volume formula for a cube is $V=s^{3}$, where $s$ is the side - length of the cube.

Step3: Calculate the new volume

Substitute $s = 4x^{5}$ into the volume formula:
$V=(4x^{5})^{3}=4^{3}\times(x^{5})^{3}$ (using the power - of - a - product rule $(ab)^{n}=a^{n}b^{n}$).
$4^{3}=64$ and $(x^{5})^{3}=x^{15}$ (using the power - of - a - power rule $(a^{m})^{n}=a^{mn}$).
So, $V = 64x^{15}$.

Answer:

$64x^{15}$