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Svetach [21]
4 years ago
9

Rewrite the rational exponent as a radical by extending the properties of integer exponents.

Mathematics
2 answers:
Aloiza [94]4 years ago
5 0

\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad  a^n\implies \cfrac{1}{a^{-n}} \\\\\\ \textit{also recall that }a^{\frac{ n}{ m}} \implies  \sqrt[ m]{a^ n}  \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}} \\\\ -------------------------------


\bf \cfrac{11^{\frac{2}{5}}}{11^{\frac{1}{4}}}\implies 11^{\frac{2}{5}}\cdot 11^{-\frac{1}{4}}\implies 11^{\frac{2}{5}-\frac{1}{4}}\implies 11^{\frac{8-5}{20}}\implies 11^{\frac{3}{20}} \\\\\\ \sqrt[20]{11^3}\implies \sqrt[20]{1331}

zimovet [89]4 years ago
3 0

the answer is 11 to the fifths power :)

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