Bài tập 5 trang 76 SGK Toán 12 NC

Bài tập 5 trang 76 SGK Toán 12 NC

a)

\(\frac{{{{\left( {\sqrt[4]{{{a^3}{b^2}}}} \right)}^4}}}{{\sqrt[3]{{\sqrt {{a^{12}}{b^6}} }}}} = \frac{{{a^3}{b^2}}}{{\sqrt[6]{{{a^{12}}{b^6}}}}} = \frac{{{a^3}{b^2}}}{{{a^2}b}} = ab\)

b)

\(\begin{array}{l}
\frac{{{a^{\frac{1}{3}}} - {a^{\frac{7}{3}}}}}{{{a^{\frac{1}{3}}} - {a^{\frac{4}{3}}}}} - \frac{{{a^{ - \frac{1}{3}}} - {a^{\frac{5}{3}}}}}{{{a^{\frac{2}{3}}} + {a^{ - \frac{1}{3}}}}}\\
 = \frac{{{a^{\frac{1}{3}}}\left( {1 - {a^2}} \right)}}{{{a^{\frac{1}{3}}}\left( {1 - a} \right)}} - \frac{{{a^{ - \frac{1}{3}}}\left( {1 - {a^2}} \right)}}{{{a^{ - \frac{1}{3}}}\left( {a + 1} \right)}}\\
 = \left( {1 + a} \right) - \left( {1 - a} \right) = 2a
\end{array}\)

-- Mod Toán 12