[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{10}^{\frac{3}{4}x}\implies \left( 10^{\frac{1}{2}} \right)^{\frac{3}{4}x}\implies \left( 10^{\frac{1}{2}} \right)^{\frac{3x}{4}}\implies (10)^{\frac{1}{2}\cdot \frac{3x}{4}}\implies (10)^{\frac{3x}{8}} \\\\\\ \sqrt[8]{10^{3x}}\implies \blacktriangleright \left( \sqrt[8]{10} \right)^{3x} \blacktriangleleft[/tex]
