Cho hàm số f(a)=a^-1/3 (căn bậc ba(a) -căn bậc ba(a^4))/a^1/8 (căn bậc tám(a^3) -căn bậc tám a^-1))

* Hướng dẫn giải

Chọn D.

Ta có

$$\begin{gathered} f\left(a\right)=\frac{a^{\frac{-1}{3}}\left(\sqrt[3]{a}-\sqrt[3]{a^4}\right)}{a^{\frac{1}{8}}\left(\sqrt[8]{a^3}-\sqrt[8]{a^{-1}}\right)}=\frac{a^{\frac{-1}{3}}\left(a^{\frac{1}{3}}-a^{\frac{4}{3}}\right)}{a^{\frac{1}{8}}\left(a^{\frac{3}{8}}-a^{\frac{-1}{8}}\right)}=\frac{a^{\frac{-1}{3}}{a}^{\frac{1}{3}}\left(1-a\right)}{a^{\frac{1}{8}}{a}^{\frac{-1}{8}}\left(a^{\frac{1}{2}}-1\right)}=\frac{\left(1-a\right)}{\sqrt{a}-1}=-\sqrt{a}-1 \\ \Rightarrow f\left({2021}^{2020}\right)=-{\left({2021}^{2020}\right)}^{\frac{1}{2}}-1=-{2021}^{1010}-1. \end{gathered}$$