[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}
\\\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}\\\\
-----------------------------\\\\[/tex]
[tex]\bf \cfrac{2^{\frac{7}{8}}}{2^{\frac{1}{4}}}\implies \cfrac{2^{\frac{7}{8}}}{1}\cdot \cfrac{1}{2^{\frac{1}{4}}}\implies 2^{\frac{7}{8}}\cdot 2^{-\frac{1}{4}}\impliedby
\begin{array}{llll}
\textit{same base}\\
\textit{add the exponents}
\end{array}
\\\\\\
2^{\cfrac{}{}\frac{7}{8}-\frac{1}{4}}\implies 2^{\frac{5}{8}}\implies \sqrt[8]{2^5}\implies \sqrt[8]{32}[/tex]
