Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\sqrt{\frac{1}{{x}^{3}}}\]
Simplify.
\[\frac{\sqrt{1}}{\sqrt{{x}^{3}}}\]
Simplify \(\sqrt{1}\) to \(1\).
\[\frac{1}{\sqrt{{x}^{3}}}\]
Simplify \(\sqrt{{x}^{3}}\) to \({({x}^{3})}^{\frac{1}{2}}\).
\[\frac{1}{{({x}^{3})}^{\frac{1}{2}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{1}{{x}^{\frac{3}{2}}}\]
1/x^(3/2)
