Question

Ultimele doua subpuncte va rog!!!

Answer 1

Răspuns:

c)$2^{\frac{37}{12}}$

d)$3$

Explicație pas cu pas:

c) $\sqrt[3]{\sqrt{16}}*\sqrt{\sqrt[3]{128}}*\sqrt{2\sqrt{8}}=\\=\sqrt[3]{\sqrt{2^4}}*\sqrt{\sqrt[3]{2^7}}*\sqrt{2\sqrt{2^3}}\\=\sqrt[3]{2^2}*\sqrt{2^{\frac{7}{3}}}*\sqrt{2*2^{\frac{3}{2}}}\\=2^{\frac{2}{3}}*2^{\frac{7}{6}}*\sqrt{2^{\frac{5}{2}}}\\=2^{\frac{2}{3}}*2^{\frac{7}{6}}*2^{\frac{5}{4}}\\=2^{\frac{37}{12}}\\=8*\sqrt[12]{2}$

d)$\sqrt{3\sqrt[5]{3}}*\sqrt[10]{9\sqrt[4]{3^5*27}}=\\=\sqrt{3*3^{\frac{1}{5}}}*\sqrt[10]{9\sqrt[4]{3^5*3^3}}\\=\sqrt{3^{\frac{6}{5}}}*\sqrt[10]{3^2*\sqrt[4]{3^8}}\\=3^{\frac{6}{10}}*\sqrt[10]{3^2*3^2}\\=3^{\frac{6}{10}}*\sqrt[10]{3^4}\\=3^{\frac{6}{10}}*3^{\frac{4}{10}}\\=3^{\frac{10}{10}}\\=3$