Simplifying Square roots(variables)

[lament hedge]

This might be the very basic basics of algebra/variables but how do you multiply x by something else when x itself doesnt exactly hve a value at default other than 1

[lament hedge]

Specifically this part, with all the X variables

[hazy raptor]

\begin{align*} \sqrt{x^3} &= \sqrt{x^2 \cdot x} \qquad \text{just like $\sqrt{500} = \sqrt{5\times 10^2}$} \ &= \sqrt{x^2} \cdot \sqrt{x} \qquad \text{just like $\sqrt{5\times 10^2} = \sqrt{5} \times \sqrt{10^2}$} \ &= |x| \cdot \sqrt{x} \qquad \text{as $ \sqrt{x^2} > 0$ even if $x < 0$} \ &= x \cdot \sqrt{x} \qquad \text{as $x > 0$ is given, so $|x| = x$} \ &= x\sqrt{x} \end{align*}