Odpowiedź:
Szczegółowe wyjaśnienie:
[tex]2 * \sqrt[3]{2\sqrt[4]{4\sqrt[5]{8} } } = 2 * \sqrt[3]{2\sqrt[4]{4\sqrt[5]{2^3} } } = 2 * \sqrt[3]{2\sqrt[4]{4((2^3)^\frac{1}{5}) } } = 2 * \sqrt[3]{2\sqrt[4]{2^2(2^\frac{3}{5}) } } = 2 * \sqrt[3]{2\sqrt[4]{2^{(2+\frac{3}{5})} } } = 2 * \sqrt[3]{2\sqrt[4]{2^{2\frac{3}{5} } } } = 2 * \sqrt[3]{2\sqrt[4]{2^{\frac{13}{5} } } } = 2 * \sqrt[3]{2((2^\frac{13}{5})^\frac{1}{4}) } = 2 * \sqrt[3]{2(2^\frac{13}{20}) } =[/tex]
[tex]= 2 * \sqrt[3]{2^{(1 +\frac{13}{20} )}} = 2 * \sqrt[3]{2^\frac{33}{20} } = 2 * ((2^\frac{33}{20})^\frac{1}{3} ) = 2 * 2^\frac{33}{60} = 2^{(1 + \frac{33}{60} )} = 2^\frac{93}{60}[/tex]
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Odpowiedź:
Szczegółowe wyjaśnienie:
[tex]2 * \sqrt[3]{2\sqrt[4]{4\sqrt[5]{8} } } = 2 * \sqrt[3]{2\sqrt[4]{4\sqrt[5]{2^3} } } = 2 * \sqrt[3]{2\sqrt[4]{4((2^3)^\frac{1}{5}) } } = 2 * \sqrt[3]{2\sqrt[4]{2^2(2^\frac{3}{5}) } } = 2 * \sqrt[3]{2\sqrt[4]{2^{(2+\frac{3}{5})} } } = 2 * \sqrt[3]{2\sqrt[4]{2^{2\frac{3}{5} } } } = 2 * \sqrt[3]{2\sqrt[4]{2^{\frac{13}{5} } } } = 2 * \sqrt[3]{2((2^\frac{13}{5})^\frac{1}{4}) } = 2 * \sqrt[3]{2(2^\frac{13}{20}) } =[/tex]
[tex]= 2 * \sqrt[3]{2^{(1 +\frac{13}{20} )}} = 2 * \sqrt[3]{2^\frac{33}{20} } = 2 * ((2^\frac{33}{20})^\frac{1}{3} ) = 2 * 2^\frac{33}{60} = 2^{(1 + \frac{33}{60} )} = 2^\frac{93}{60}[/tex]