Cho hàm số fa=a23a−23−a3a18a38−a−18 với a>0, a≠1. Giá trị của M=f20192018 là

Đáp án D

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

Khi đó . $M=f\left({2019}^{2018}\right)=-{\left({2019}^{2018}\right)}^{\frac{1}{2}}-1=-{2019}^{1009-1}$