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![\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}} \\\\\\ a^{-\frac{{ n}}{{ m}}} \implies \cfrac{1}{a^{\frac{{ n}}{{ m}}}} \implies \cfrac{1}{\sqrt[{ m}]{a^{ n}}}\qquad\qquad \cfrac{1}{\sqrt[{ m}]{a^{ n}}}= \cfrac{1}{a^{\frac{{ n}}{{ m}}}}\implies a^{-\frac{{ n}}{{ m}}} \\\\ -------------------------------](/tpl/images/0112/3908/23e95.png)
![\bf \cfrac{\sqrt[3]{5}}{\sqrt[4]{5}}\implies \cfrac{\sqrt[3]{5^1}}{\sqrt[4]{5^1}}\implies \cfrac{5^{\frac{1}{3}}}{5^{\frac{1}{4}}}\implies 5^{\frac{1}{3}}\cdot 5^{-\frac{1}{4}}\implies 5^{\frac{1}{3}-\frac{1}{4}}\implies 5^{\frac{4-3}{12}} \\\\\\ 5^{\frac{1}{12}}\implies \sqrt[12]{5^1}\implies \sqrt[12]{5}](/tpl/images/0112/3908/a8ada.png)
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