Mathematics, 14.07.2019 18:30 myaxo
Rewrite the rational exponent as a radical by extending the properties of integer exponents. 11 to the two fifths power over 11 to the one fourth power
Answers: 2
![\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}} \\\\ -------------------------------](/tpl/images/0089/6170/0c16b.png)
![\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}](/tpl/images/0089/6170/47d56.png)
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