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Question Number 197393 by mathlove last updated on 16/Sep/23

Answered by Frix last updated on 16/Sep/23

$$\frac{3\times 5\sqrt[3]{2^2\sqrt[3]{2^{6}3}}+3\times 7\sqrt[3]{2\times 3^2\sqrt[3]{3^4}}}{\sqrt[3]{2^{2}3\sqrt[3]{2^{3}3}+2\times 3\sqrt[3]{3\times 5^3}}}=$$$$=\frac{2^{\frac{4}{3}}{3}^{\frac{10}{9}}5+2^{\frac{1}{3}}{3}^{\frac{19}{9}}7}{{(2^3{3}^{\frac{4}{3}}+2\times 3^{\frac{4}{3}}5)}^{\frac{1}{3}}}=\frac{2^{\frac{1}{3}}{3}^{\frac{10}{9}}(2\times 5+3\times 7)}{{\left(2\times 3^{\frac{4}{3}}(4+5)\right)}^{\frac{1}{3}}}=$$$$=\frac{2^{\frac{1}{3}}{3}^{\frac{10}{9}}31}{2^{\frac{1}{3}}{3}^{\frac{10}{9}}}=31$$

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