Bài tập 18 trang 81 SGK Toán 12 NC

a)

\(\sqrt[4]{{{x^2}\sqrt[3]{x}}} = {\left( {{x^2}{x^{\frac{1}{3}}}} \right)^{\frac{1}{4}}} = {\left( {{x^{\frac{7}{3}}}} \right)^{\frac{1}{4}}} = {x^{\frac{7}{{12}}}}\)

b)

\(\begin{array}{l}
\sqrt[5]{{\frac{b}{a}\sqrt[3]{{\frac{a}{b}}}}} = {\left( {\frac{b}{a}{{\left( {\frac{a}{b}} \right)}^{\frac{1}{3}}}} \right)^{\frac{1}{5}}}\\
 = {\left( {{{\left( {\frac{a}{b}} \right)}^{ - 1}}{{\left( {\frac{a}{b}} \right)}^{\frac{1}{3}}}} \right)^{\frac{1}{5}}} = {\left( {{{\left( {\frac{a}{b}} \right)}^{\frac{{ - 2}}{3}}}} \right)^{\frac{1}{5}}}\\
 = {\left( {\frac{a}{b}} \right)^{\frac{{ - 2}}{{15}}}}
\end{array}\)

c)

\(\begin{array}{l}
\sqrt[3]{{\frac{2}{3}\sqrt[3]{{\frac{2}{3}}}.\sqrt {\frac{2}{3}} }} = {\left( {\frac{2}{3}{{\left( {\frac{2}{3}} \right)}^{\frac{1}{3}}}{{\left( {\frac{2}{3}} \right)}^{\frac{1}{6}}}} \right)^{\frac{1}{3}}}\\
 = {\left( {{{\left( {\frac{2}{3}} \right)}^{1 + \frac{1}{3} + \frac{1}{6}}}} \right)^{\frac{1}{3}}} = {\left( {{{\left( {\frac{2}{3}} \right)}^{\frac{2}{3}}}} \right)^{\frac{1}{3}}} = {\left( {\frac{2}{3}} \right)^{\frac{1}{2}}}
\end{array}\)

d)

\(\begin{array}{l}
\sqrt {a\sqrt {a\sqrt {a\sqrt a } } } :{a^{\frac{{11}}{{16}}}}\\
 = \left( {{a^{\frac{1}{2}}}.{a^{\frac{1}{4}}}.{a^{\frac{1}{8}}}.{a^{\frac{1}{{16}}}}} \right):{a^{\frac{{11}}{{16}}}}\\
 = {a^{\frac{{15}}{{16}}}}:{a^{\frac{{11}}{{16}}}} = {a^{\frac{1}{4}}}
\end{array}\)

-- Mod Toán 12 HỌC247