3. Выполните действия: 1) 2·2^(1/2)·2^(1/4)·2^(1/8); 2) ((2^(2/3))/(4^(5/6)))^3; 3) √((3·∛9)/⁴√27); 4) (a^(2/3)·a^(-5/4))/(a^(3/2)·a^(-1/3)); 5) ((a²)^(1/3))^(3/5); 6) (3^(1/3)·7^(1/3))/(9^(1/3)).

Question

Вопрос:

Accepted Answer

\(2\cdot2^{1/2}\cdot2^{1/4}\cdot2^{1/8}=2^{1+1/2+1/4+1/8}=2^{15/8}\).
\(\left(\frac{2^{2/3}}{4^{5/6}}\right)^3=\left(\frac{2^{2/3}}{2^{5/3}}\right)^3=(2^{-1})^3=\frac18\).
\(\sqrt{\frac{3\sqrt[3]9}{\sqrt[4]{27}}}=\sqrt{3^{1+2/3-3/4}}=\sqrt{3^{11/12}}=3^{11/24}\).
\(\frac{a^{2/3}a^{-5/4}}{a^{3/2}a^{-1/3}}=a^{2/3-5/4-3/2+1/3}=a^{-7/4}\).
\(\left((a^2)^{1/3}\right)^{3/5}=a^{2/3\cdot3/5}=a^{2/5}\).
\(\frac{3^{1/3}7^{1/3}}{9^{1/3}}=\left(\frac{21}{9}\right)^{1/3}=\sqrt[3]{\frac73}\).

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