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Zjednodušenie výrazu s odmocninami
Zjednoduš výraz \( \sqrt{a \cdot \sqrt[3]{a} \cdot \sqrt[4]{a}} \) pre \( a>0 \) a zapíš ho ako odmocninu.
\( =\left(a^{\frac{19}{12}}\right)^{\frac{1}{2}}=a^{\frac{19}{12} \cdot \frac{1}{2}}=a^{\frac{19}{24}}=\sqrt[24]{a^{19}} \)
\( =\left(a^{\frac{19}{12}}\right)^{\frac{1}{2}}=a^{\frac{19}{12} \cdot \frac{1}{2}}=a^{\frac{19}{25}}=\sqrt[25]{a^{19}} \)
\( =\left(a^{\frac{19}{12}}\right)^{\frac{1}{2}}=a^{\frac{19}{12} \cdot \frac{1}{2}}=a^{\frac{18}{24}}=\sqrt[24]{a^{18}} \)
\( =\left(a^{\frac{19}{12}}\right)^{\frac{1}{2}}=a^{\frac{19}{12} \cdot \frac{1}{2}}=a^{\frac{20}{24}}=\sqrt[24]{a^{20}} \)