8. the side length of a cube is $x^{-2}$ in. what is the volume of the cube?

Explanation:

Step1: Recall volume formula for cube

The volume $V$ of a cube with side - length $s$ is $V = s^{3}$.

Step2: Substitute side - length into formula

Here, $s=x^{-2}$, so $V=(x^{-2})^{3}$.

Step3: Apply power - of - a - power rule

According to the power - of - a - power rule $(a^{m})^{n}=a^{mn}$. So, $(x^{-2})^{3}=x^{-2\times3}=x^{-6}=\frac{1}{x^{6}}$.

Answer:

$\frac{1}{x^{6}}$