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# Rewrite the rational exponent as a radical by extending the properties of integer exponents. (2 points) 2 to the 7 over 8 power, all over 2 to the 1 over 4 power

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