[tex]\bf a^{\frac{{ n}}{{ m}}} \iff \sqrt[{ m}]{a^{ n}}
\\\\\\
\cfrac{a^{{ m}}}{a^{{ n}}}\implies \cfrac{a^{{ m}}}{1}\cdot \cfrac{1}{a^{{ n}}}\implies a^{{ m}}\cdot a^{-{ n}}\implies a^{{{ m}}{-{ n}}}\\\\
-----------------------------\\\\
thus
\\\\\\
\cfrac{5\sqrt{x}}{20x^3}\implies \cfrac{5\sqrt[2]{x^1}}{20x^3}\implies \cfrac{5x^{\frac{1}{2}}}{20x^3}\implies \cfrac{5}{20x^3}\cdot \cfrac{x^{\frac{1}{2}}}{1}
\\\\\\
[/tex]
[tex]\bf \cfrac{5}{20}\cdot \cfrac{1}{x^3}\cdot \cfrac{1}{x^{-\frac{1}{2}}}\implies \cfrac{1}{4}\cdot \cfrac{1}{x^3\cdot x^{-\frac{1}{2}}}\implies \cfrac{1}{4}\cdot \cfrac{1}{x^{3-\frac{1}{2}}}
\\\\\\
\cfrac{1}{4}\cdot \cfrac{1}{x^{\frac{5}{2}}}\implies \cfrac{1}{4}\cdot \cfrac{1}{\sqrt[2]{x^5}}\implies \cfrac{1}{4\sqrt{x^5}}[/tex]
