[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt{x}\cdot 4\sqrt{x}\implies x^{\frac{1}{2}}\cdot 4x^{\frac{1}{2}}\implies 4x^{\frac{1}{2}}x^{\frac{1}{2}}\implies 4x^{\frac{1}{2}+\frac{1}{2}}\implies 4x^{\frac{2}{2}}\implies 4x[/tex]
