Cho hàm số f(a)=a−13(a3−a43)a18(a38−a−18) với a>0,a≠1. Tính giá trị M=f(20212020).

Ta có: \(f\left( a \right) = \frac{{{a^{\frac{{ - 1}}{3}}}\left( {\sqrt[3]{a} - \sqrt[3]{{{a^4}}}} \right)}}{{{a^{\frac{1}{8}}}\left( {\sqrt[8]{{{a^3}}} - \sqrt[8]{{{a^{ - 1}}}}} \right)}} = \frac{{{a^{\frac{{ - 1}}{3}}}\left( {{a^{\frac{1}{3}}} - {a^{\frac{4}{3}}}} \right)}}{{{a^{\frac{1}{8}}}\left( {{a^{\frac{3}{8}}} - {a^{\frac{{ - 1}}{8}}}} \right)}} = \frac{{{a^{\frac{{ - 1}}{3}}}{a^{\frac{1}{3}}}\left( {1 - a} \right)}}{{{a^{\frac{1}{8}}}{a^{\frac{{ - 1}}{8}}}\left( {{a^{\frac{1}{2}}} - 1} \right)}} = \frac{{\left( {1 - a} \right)}}{{\sqrt a - 1}} = - \sqrt a - 1\)

⇒f(20212020)=−(20212020)12−1=−20211010−1.

Đáp án D