Giải Bài tập 2 trang 13 Toán 11 tập 2 Chân trời

a) $3.\sqrt{3}.\sqrt[4]{3}.\sqrt[8]{3}=3.3^{\frac{1}{2}}.3^{\frac{1}{4}}.3^{\frac{1}{8}}=3^{1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}}=3^{\frac{15}{8}}$

b) $\sqrt{a.\sqrt{a.\sqrt{a}}} = \sqrt{a.\sqrt{a.a^{\frac{1}{2}}}}=\sqrt{a.\sqrt{a^{1+\frac{1}{2}}}}=\sqrt{a.\sqrt{a^{\frac{3}{2}}}}$

$= \sqrt{a.a^{\frac{3}{4}}} = \sqrt{a^{1+\frac{3}{4}}}=\sqrt{a^{\frac{7}{4}}} = a^{\frac{7}{8}}$

c) $\frac{\sqrt{a}.\sqrt[3]{a}.\sqrt[4]{a}}{(\sqrt[5]{a})^{3}.a^{\frac{2}{5}}} = \frac{a^{\frac{1}{2}}.a^{\frac{1}{3}}.a^{\frac{1}{4}}}{a^{\frac{3}{5}}.a^{\frac{2}{5}}}= \frac{a^{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}}}{a^{\frac{3}{5}+\frac{2}{5}}}=\frac{a^{\frac{13}{12}}}{a}=a^{\frac{13}{12}-1}=a^{\frac{1}{12}}$