Simplify \(\sqrt{{y}^{3}}\) to \({({y}^{3})}^{\frac{1}{2}}\).
\[\frac{{x}^{2}{({y}^{3})}^{\frac{1}{2}}}{2x{y}^{5}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{x}^{2}{y}^{\frac{3}{2}}}{2x{y}^{5}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[\frac{{x}^{2-1}{y}^{\frac{3}{2}-5}}{2}\]
Simplify \(2-1\) to \(1\).
\[\frac{{x}^{1}{y}^{\frac{3}{2}-5}}{2}\]
Simplify \(\frac{3}{2}-5\) to \(-\frac{7}{2}\).
\[\frac{{x}^{1}{y}^{-\frac{7}{2}}}{2}\]
Use Rule of One: \({x}^{1}=x\).
\[\frac{x{y}^{-\frac{7}{2}}}{2}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{x\times \frac{1}{{y}^{\frac{7}{2}}}}{2}\]
Simplify \(x\times \frac{1}{{y}^{\frac{7}{2}}}\) to \(\frac{x}{{y}^{\frac{7}{2}}}\).
\[\frac{\frac{x}{{y}^{\frac{7}{2}}}}{2}\]
Simplify.
\[\frac{x}{2{y}^{\frac{7}{2}}}\]
x/(2*y^(7/2))
